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  • 1
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    Stochastic environmental research and risk assessment 11 (1997), S. 193-210 
    ISSN: 1436-3259
    Keywords: Turbulence ; sediment ; fluvial ; river ; bursting process ; statistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract Entrainment of sediment particles from channel beds into the channel flow is influenced by the characteristics of the flow turbulence which produces stochastic shear stress fluctuations at the bed. Recent studies of the structure of turbulent flow has recognized the importance of bursting processes as important mechanisms for the transfer of momentum into the laminar boundary layer. Of these processes, the sweep event has been recognized as the most important bursting event for entrainment of sediment particles as it imposes forces in the direction of the flow resulting in movement of particles by rolling, sliding and occasionally saltating. Similarly, the ejection event has been recognized as important for sediment transport since these events maintain the sediment particles in suspension. In this study, the characteristics of bursting processes and, in particular, the sweep event were investigated in a flume with a rough bed. The instantaneous velocity fluctuations of the flow were measured in two-dimensions using a small electromagnetic velocity meter and the turbulent shear stresses were determined from these velocity fluctuations. It was found that the shear stress applied to the sediment particles on the bed resulting from sweep events depends on the magnitude of the turbulent shear stress and its probability distribution. A statistical analysis of the experimental data was undertaken and it was found necessary to apply a Box-Cox transformation to transform the data into a normally distributed sample. This enabled determination of the mean shear stress, angle of action and standard error of estimate for sweep and ejection events. These instantaneous shear stresses were found to be greater than the mean flow shear stress and for the sweep event to be approximately 40 percent greater near the channel bed. Results from this analysis suggest that the critical shear stress determined from Shield's diagram is not sufficient to predict the initiation of motion due to its use of the temporal mean shear stress. It is suggested that initiation of particle motion, but not continuous motion, can occur earlier than suggested by Shield's diagram due to the higher shear stresses imposed on the particles by the stochastic shear stresses resulting from turbulence within the flow.
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  • 2
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    Pure and applied geophysics 130 (1989), S. 547-569 
    ISSN: 1420-9136
    Keywords: Turbulence ; atmospheric turbulence ; clear air turbulence ; middle atmosphere ; heat flux
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The physical nature of motions with scales intermediate between approximately isotropic turbulence and quasi-linear internal gravity waves is not understood at the present time. Such motions play an important role in the energetics of small scales processes, both in the ocean and in the atmosphere, and in vertical transport of heat and constituents. This scale range is currently interpreted either as a saturated gravity waves field or as a buoyancy range of turbulence. We first discuss some distinctive predictions of the classical (Lumley, Phillips) buoyancy range theory, recently improved (Weinstock, Dalaudier and Sidi) to describe potential energy associated with temperature fluctuations. This theory predicts the existence of a spectral gap in the temperature spectra and of an upward mass flux (downward buoyancy and heat fluxes), strongly increasing towards large scales. These predictions are contrasted with an alternate theory, assuming “energetically insignificant” buoyancy flux, proposed by Holloway. Then we present experimental evidences of such characteristic features obtained in the lower stratosphere with an instrumented balloon. Spectra of temperature, vertical velocity, and cospectra of both, obtained in homogeneous, weakly turbulent regions, are compared with theoretical predictions. These results are strongly consistent with the improved classical buoyancy range theory and support the existence of a significant downward heat flux in the buoyancy range. The theoretical implications of the understanding of this scale range are discussed. Many experimental evidences consistently show the need for an anisotropic theory of the buoyancy range of turbulence.
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  • 3
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    Pure and applied geophysics 118 (1980), S. 494-527 
    ISSN: 1420-9136
    Keywords: MST radar ; Gravity waves ; Turbulence ; Stratospheric structure
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Powerful VHF radars are capable of almost continuously monitoring the threedimensional velocity vector and the distribution of turbulence in the middle atmosphere, i.e. the stratosphere and mesosphere. Methods of radar investigations of the middle atmosphere are outlined and the basic parameters, mean and fluctuating velocities as well as reflectivity and persistency of atmospheric structures, are defined. Results of radar investigations are described which show that the tropopause level as well as a criterion on the stability of the lower stratosphere can be deduced. Besides mean wind velocities, VHF radars can measure instantaneous velocities due to acoustic gravity waves. The interaction of gravity waves with the background wind is discussed, and it is shown that cumulus convection is an effective source of gravity waves in the lower stratosphere. The vertical microstructure of the stratosphere, manifesting itself in thin stratified sheets in which temperature steps occur, is investigated by applying knowledge from investigations of the oceanic thermocline. Possible origins, like shear generation and lateral convection of the microstructure of the stratosphere, are discussed. Observations of gravity waves in the mesosphere are reviewed and their connection with turbulence structures is pointed out. Finally, some open questions which could be answered by further VHF radar investigations are summarized.
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  • 4
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    Pure and applied geophysics 120 (1982), S. 95-107 
    ISSN: 1420-9136
    Keywords: Boundary layer ; Spectral density ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract We have carried out a series of recordings reproducing the small scale structures of temperature and windspeed within the boundary layer. The results obtained have been processed by computer and a direct comparison made between the slope of the spectral density functions and the theoretical slopen=5/3 defining the turbulence in the region of the inertial subrange. The measurements made at various altitudes on thin atmospheric samples demonstrate the variability of the spectral density slope with altitude. The hypotheses put forward by A. M. Obukhov, R. Bolgiano, G. H. Shur, P. Misme, A. Monin or S. Panchev, for example, enable the spectral variations and certain discontinuities in the turbulence observed during the experiments, within and beyond the boundary layer, to be explained.
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  • 5
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    Pure and applied geophysics 120 (1982), S. 648-661 
    ISSN: 1420-9136
    Keywords: Atmospheric turbulence ; Entrainment ; Turbulence ; Karman constant
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract This paper extends the theory of the entity and entrainment model of turbulence to obtain a numerical value of von Karman's constant,k=0.37. The formula is, $$k = (2a^3 /A)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} \ln \beta $$ where,a=1/12 is the entrainment constant,A=1 is the turbulent decay constant, and β is the ratio in height of the successive self-similar layers of the theory, where β is evaluated as β=e 2. These new values fork and β improve the surface roughness length estimates derived from this theory.
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  • 6
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    Pure and applied geophysics 120 (1982), S. 758-771 
    ISSN: 1420-9136
    Keywords: Diffusion ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Dye plumes were generated at three depths in the seasonal thermocline between 7 and 11 m, 22 km south of Key West on 21 August 1980 and photographed at about 10 second intervals with an underwater camera system. Eleven pairs of consecutive pictures are analyzed to determine the mean current vertical shear and the width of the plumes by positioning reference points relative to the rod attached to the camera system. The relative distances of reference points are calibrated with the stereophotogrammetric method for one pair. The eddy diffusivity is calculated by use of a model of turbulent diffusion developed byTaylor (1921). Its values range from 5 to 25 cm2s−1 for the plume widths ranging from 33 to 132 cm. The Richardson number is calculated for each pair of pictures with the vertical density gradient estimated from temperature profiles. Its values are higher than the critical value of 0.25 except for one case. The diffusivity was higher by orders of magnitude than the molecular one and indicates the presence of turbulence together with billow like features of the plumes in spite of high Richardson numbers. This suggests that the billow turbulence might be caused by effects of surface gravity waves and not by the Kelvin-Helmholtz instability.
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  • 7
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    Boundary layer meteorology 87 (1998), S. 459-480 
    ISSN: 1573-1472
    Keywords: Coherence model ; Spatial coherence ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Wind speed measurements from the test site at Rutherford Appleton Laboratory have been evaluated with respect to the spatial coherence function. The experimental arrangement provides coherence information for separation distances of 62, 80 and 102 m. These are at least three times greater than the measurement heights of 18 m and 18.7 m. Based on these experimental data and data published in the literature, different theoretical formulations are compared and a new, but simple, model for longitudinal and lateral coherence is proposed. At large separations the turbulent wind field is not isotropic, theoretical models to describe the coherence function for such distances are not available. The new model we propose builds on the classical exponential approach. It takes into account the influence of turbulence intensity and models the angular dependence of horizontal coherence. It is found that, for constant turbulence intensity, the lateral coherence decay becomes independent of the mean wind speed.
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  • 8
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    Boundary layer meteorology 89 (1998), S. 285-316 
    ISSN: 1573-1472
    Keywords: Boundary layer ; Heterogeneous terrain ; Roughness length ; Surface fluxes ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The aim of this work is to present experimentally evaluated effective roughnesses (zoe) of a partly forested landscape. Although the ratio of boundary-layer height to obstacle size was only of the order of 50, there still seemed to exist a height range of 75–200 m where surface-layer similarity was approximately valid. Attempts were made to use conventional wind profile analysis to evaluate zoe, but the small height range and the large number of variables initially led to unacceptable uncertainties. Fixing the displacement height zd, rather than fitting it, reduced the data scatter to an acceptable level. The profile-derived roughness lengths zop obtained in this way were in good agreement with previous work, and with an alternative roughness length estimate zof for which flux-derived profile parameters u* and θ* were used. This implies that the profile-derived roughnesses were consistent with the measured surface-layer momentum flux. Comparison of both roughness estimates also yielded an improved estimate of the displacement height. Besides this, the authors tested a landscape roughness evaluation method which makes use of the gustiness parameter Tu = σu/U in the surface layer. The results obtained by this method were in fair agreement with the profile-derived data. In previous work, the gustiness method was advocated because it could be used at relatively low levels, perhaps even within the roughness sub-layer. At the present measuring site, this was not the case as the gustiness method was only valid in an approximate way, and for a limited height range.
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  • 9
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    Boundary layer meteorology 77 (1996), S. 1-20 
    ISSN: 1573-1472
    Keywords: Turbulence ; Water vapor ; Turbulent flux ; Bulk Coefficient ; HEIFE ; Desert ; Similarity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Observations of surface-layer turbulence and turbulent fluxes were made over a desert in northwestern China as a part of HEIFE (HEIhe river Field Experiment). These show that the normalized variations of the vertical wind component and of the air temperature obey Monin-Obukhov similarity well, especially in free convective conditions. However, the variations of specific humidity do not obey Monin-Obukhov similarity. Mean bulk transfer coefficients of sensible heat and momentum flux are obtained as functions of stability over a wide stability range from the observed data of turbulent fluxes and mast profiles. However, the bulk transfer coefficient for water vapor could not be obtained because of the large scatter of the data. In free convective conditions, the sensible heat flux was found to be approximately proportional to the 1.4 power of temperature difference between the surface and 20m. The bulk transfer coefficient of sensible heat is also obtained as a function of the bulk Richardson number for practical convenience.
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  • 10
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    Boundary layer meteorology 83 (1997), S. 285-309 
    ISSN: 1573-1472
    Keywords: Adjoint ; Data assimilation ; Turbulence ; Complex terrain
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract This paper describes an adjoint method for data assimilation intoupstream boundary conditions of numerical modelsusing optimal control theory. Mathematical formalisms are given along with the numerical implementation of the schemein a column model of the atmospheric boundary layer. The optimized mean and turbulence profiles are used as an upstream solutionin a model of turbulent flow in complex terrain. To contrast thiswith other methods, two solutions for flow over an isolatedhill are calculated, one with an optimized upstream solution andone with a simple surface-layer formulation for the upstream solution.These two solutions are compared to observations and analytical theory. The adjoint optimization method is shown to producesolutions of flow in complex terrain that are substantively differentat the two solutions, with the optimized solution giving more accurate results.
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  • 11
    ISSN: 1573-1472
    Keywords: Turbulence ; Canopies ; Temperature ramps ; Renewal models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Sensible heat, latent heat, and other scalar fluxes cannot be measuredwithin short dense canopies, e.g., straw mulches, with standard approachessuch as eddy correlation, Bowen ratio-energy balance, aerodynamic, andvariance methods. However, recently developed surface renewal models, thatare based on the fact that most of the turbulent transfer within and abovecanopies is associated with large-scale coherent eddies, which are evidentas ramp patterns in scalar time series, offer a feasible solution. Wepresent a new air renewal model that calculates sensible heat flux atdifferent heights within and above a canopy from the average cubictemperature structure function, sampled at a moderate rate, and measuredaverage friction velocity. The model is calibrated and tested with datameasured above and within a Douglas-fir forest and above a straw mulch andbare soil. We show that the model describes half-hour variations ofsensible heat flux very well, both within the canopy and roughnesssublayers and in the inertial sublayer, for stable and unstable atmosphericconditions. The combined empirical coefficient that appears in the modelhas an apparently universal value of about 0.4 for all surfaces andheights, which makes application of the model particularly simple. Themodel is used to predict daytime and nighttime sensible heat flux profileswithin the straw mulch and within a small bare opening in the mulch.
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  • 12
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    Boundary layer meteorology 84 (1997), S. 411-425 
    ISSN: 1573-1472
    Keywords: Trajectories ; Turbulence ; Dispersion ; Diffusion ; Numerical models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Among well-mixed multi-dimensional Lagrangian stochastic (LS) dispersion models, we observe that those in poorest agreement with observations produce ‘spiralling trajectories,’ with an associated reduction in dispersion. We therefore investigate statistics of increments dθ ' to the orientation θ'= arctan(W'/U') of the Lagrangian velocity-fluctuation vector – as a possible means to distinguish the better LS models within the well-mixed class. ‘Zero-spin’ models, having 〈 dθ'〉 = 0, are found to provide best agreement with observations. It is not clear however, whether imposition of the zero-spin property selects (in conjunction with the well-mixed condition) a unique model.
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  • 13
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    Boundary layer meteorology 85 (1997), S. 197-222 
    ISSN: 1573-1472
    Keywords: Turbulence ; Chemistry ; Closure ; Convective boundary layer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract We study the interactions of chemistry and turbulent mixing of tracersin the convective boundary layer with a second-order closure model,including higher order chemistry terms. In order to limit the number of predictive equations we prescribe the profiles for ¯w¯Θ, ¯w¯θ ¯θ and the lengthscale l. However, for model validation we treat temperature and humidity asinert tracers, and compare the results with profiles observed during theAir Mass Transformation Experiment, and with similarity expressions for thesurface layer. We find good agreement of the mean profiles, but the (co-)variances are slightly underpredicted. Furthermore, the model usesdiagnostic equations expressing third moments of concentration in terms ofsecond moments and their vertical derivatives. They are compared withlarge-eddy model results, showing good agreement and, therefore, thesimplifications are justified. The model is applied to the transport of two gases subject to one bimolecular reaction. The importance of concentration correlations on themean transformation rate is studied. For two gases diffusing in oppositedirections we find for moderate and fast chemistry a 50% and90% decreased transformation rate due to the negatively correlatedconcentrations. These values are similar to large-eddy results of Schumannand Sykes et al. For two bottom-up tracers we find that the covariance ofboth reactive species is either positive or negative, increasing or reducingthe effective transformation rate depending on the Damköhler number (the ratio of the turbulent and the chemistry timescale). A significantdirect influence of chemistry on the flux divergence is found in bothcases. According to the model the effective transport to mid-levels of theboundary layer is increased when two reactive tracers diffuse in oppositedirections, and decreased in the case of two bottom-up tracers.
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  • 14
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    Boundary layer meteorology 86 (1998), S. 63-87 
    ISSN: 1573-1472
    Keywords: Stratocumulus ; Mass flux ; Lateral entrainment ; Turbulence ; Conditional sampling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A mass-flux approach is applied to observational data obtained in a convective boundary layer topped with stratocumulus clouds. The observational data were obtained from aircraft measurements during the Atlantic Stratocumulus Transition Experiment (ASTEX). A conditional sampling method is used to calculate average updraft and downdraft values. The vertical fluxes calculated with the mass-flux approach are found to be proportional to the real (measured) fluxes, with a proportionality factor being about 0.6. This value is predicted by theory for two variables having a joint Gaussian distribution function; proportionality factor = 2π-1 ≈ 0.637. The horizontal fractional entrainment and detrainment rates calculated from the data (ε ≈ 1–2 × 10-2 m-1) are an order of magnitude higher than the rates obtained by large eddy simulations for cumulus convection (ε ≈ 2–3 × 10-3 m-1) and two orders of magnitude higher than those used in modelling cumulus convection with a mass-flux scheme in an operational weather forecast model (ε ≈ 3 × 10-4 m-1). A numerical mass-flux model for the thermodynamics was developed and showed that results are in good agreement when compared with measured profiles of the liquid water content.
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  • 15
    ISSN: 1573-1472
    Keywords: Turbulence ; Surface temperature ; Surface inhomogeneity ; Source area
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Turbulence characteristics, vertical profiles of wind velocity u(z) and air temperature T(z), and also spatial variations in steppe surface radiation temperature Tr(x) are measured simultaneously. A marked effect of Tr(x) characteristics on the turbulence characteristics and T(z) profiles is observed in the lower part of the atmospheric surface layer. We suggest that variability in Tr(x) noticeably influences the surface-layer temperature field and leads to scatter in the values of the universal functions obtained by different authors; effects of Tr(x) are not accounted for in similarity theory. The introduction of the value of temperature zero-plane displacement dT in the calculation formulae (to determine temperature flux) noticeably improves the agreement between calculated and measured (by eddy-correlation method) results. The influence of footprint (or Source Area) on the obtained results leads to noticeable scatter in the data obtained from measurements of atmospheric turbulence.
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  • 16
    ISSN: 1573-1472
    Keywords: Turbulence ; Convective boundary layer ; Clear air radar observations ; Coherent organizations ; Radar-aircraft joint observations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract The scientific objective of the TRAC experiment (Turbulence Radar Aircraft Cells) was to investigate the respective roles played by small-scale turbulence and coherent structures in the vertical transfer within the atmospheric boundary layer (ABL). Field research held in June 1993 in France was based on coupled aircraft and Doppler radar measurements. The results discussed here are mainly focused on the evaluation of the performance of the radar in the 3D description of the clear air ABL, which was the technical goal of TRAC. During the experiment, the radar was able to provide continuous and coherent echo fields over a range of several tens of kilometres, extending up to about 3 km. Good agreement was obtained in the ABL between the radar-derived turbulent quantities and airborne measurements. As depicted by the reflectivity fields, coherent organizations were found to be a common feature of the eleven ABL cases analyzed. These organizations evolved during the day between a banded structure and a cellular pattern. A very weak correlation was found between the reflectivity field and the atmospheric parameters measured by the aircraft. However, in terms of characteristic scale, the reflectivity field appeared to be strongly related to the water vapour field. The inhomogeneity induced by the coherent circulations questions the representativity of one-dimensional sampling of these 3D fields and suggests the need to adapt the traditional statistical approach of the ABL.
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  • 17
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    Boundary layer meteorology 86 (1998), S. 233-256 
    ISSN: 1573-1472
    Keywords: Lidar ; Remote sensing ; Turbulence ; Velocity statistics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Coherent Doppler lidar measurements of wind statistics in the boundary layer are presented. The effects of the spatial averaging by the lidar pulse are removed using theoretical corrections and computer simulations. This permits unbiased estimates of velocity variance, spatial velocity structure functions, energy dissipation rate, and other point statistics of the velocity field.
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  • 18
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    Boundary layer meteorology 86 (1998), S. 333-344 
    ISSN: 1573-1472
    Keywords: Turbulence ; Dispersion model ; Non-uniqueness ; Plant canopy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Lagrangian stochastic models, quadratic in velocity and satisfying the well-mixed condition for two-dimensional Gaussian turbulence, are used to make predictions of scalar dispersion within a model plant canopy. The non-uniqueness associated with satisfaction of the well-mixed condition is shown to be non-trivial (i.e. different models produce different predictions for scalar dispersion). The best agreement between measured and predicted mean concentrations of scalars is shown to be obtained with a small sub-class of ‘optimal’ models. This sub-class of ‘optimal’ models includes Thomson's model (J. Fluid Mech. 180, 529–556, 1987), the simplest model that satisfies the well-mixed condition for Gaussian turbulence, but does not include two other models identified recently as being in optimal agreement with the measured spread of tracers in a neutral boundary layer. It is therefore demonstrated that such models are not universal, i.e. applicable to a wide range of flows without readjustment of model parameters. Predictions for scalar dispersion in the model plant canopy are also obtained using the model of Flesch and Wilson (Boundary-Layer Meteorol. 61, 349–374, 1992). It is shown that, when used with a Gaussian velocity distribution or a maximum-missing-information velocity distribution, which accounts for the measured skewness and kurtosis of velocity statistics, the agreement between predictions obtained using the model of Flesch and Wilson and measurements is as good as that obtained using Thomson's model.
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  • 19
    ISSN: 1573-1472
    Keywords: Lagrangian decorrelation time scales ; Structure function constant ; Turbulence ; Lagrangian spectrum constant
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    Topics: Geosciences , Physics
    Notes: Abstract A new method for deriving the Lagrangian decorrelation time scales for inhomogeneous turbulence is described. The expression for the time scales here derived for the convective boundary layer is compared to those estimated by Hanna during the Phoenix experiment. Then the values of C0, the Lagrangian velocity structure function constant, and of Bi, the Lagrangian velocity spectrum constant, were evaluated from the Eulerian velocity spectra and from the Lagrangian time scales derived, under unstable conditions, from Taylor's statistical diffusion theory. The numerical coefficient of the lateral and vertical Lagrangian spectra in the inertial subrange was found equal to 0.21, in good agreement with previous experimental estimates.
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  • 20
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    Boundary layer meteorology 87 (1998), S. 1-25 
    ISSN: 1573-1472
    Keywords: Kites ; Atmospheric measurements ; Turbulence ; Profiling ; Ozone
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract This paper presents the capabilities and limitations of using state-of-the-art kites for atmospheric research. A brief historical review of the subject is first presented, followed by an outline of the current status of kite-borne measurement technology. The utility of the technique is then illustrated by presenting a series of recent measurements made using kite-borne technology. A summary of the advantages and limitations of kite-based measurements relative to other technologies is provided for reference.
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  • 21
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    Boundary layer meteorology 91 (1999), S. 227-257 
    ISSN: 1573-1472
    Keywords: Coastal boundary layer ; Initialisation ; Mesoscale model ; Sea model breeze ; Thermal internal boundary layer ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A numerical two-dimensional-mesoscale model with a level 1.5 closure scheme for turbulence is described. The model is used to simulate the boundary layer over coastal complex terrain. Meteorological data available from the Øresund land-sea-land terrain experiment are used to study the performance of the model. The model could simulate generally observed complexities in the mean wind and temperature fields. Internal boundary layers over the water and land surfaces were identified by the height of lowest value in the turbulence kinetic energy profile and this showed good agreement with radiosonde (RS) observations. Some disagreements with the data were also noticed, especially near the surface. The wind speed was over-predicted. Attempts were made to improve the model performance by adopting different schemes for model initialisation. Results showed that initialisation with an early model start time and observed wind profile near the inflow boundary improved the performance. The wind speed over-prediction could be further minimised by using a more realistic objective initialisation scheme. The problem centred around the proper estimation of the turbulent diffusion coefficient K through the closure scheme. Despite using the most popular empirical relationships in the level 1.5 closure scheme, these differences persisted. While this needs further investigation, the present model can be used to supply wind fields for practical purposes such as air pollution calculations.
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  • 22
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    Boundary layer meteorology 91 (1999), S. 483-493 
    ISSN: 1573-1472
    Keywords: Turbulence ; Flow distortion ; Sonic anemometers
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    Topics: Geosciences , Physics
    Notes: Abstract We carried out measurements to test a simple theory of the effect of probe-induced flow distortion on turbulence measurements. We used two three-component sonic anemometers mounted 1.8m apart at a height of 6.7 m. Behind one was a horizontal circular cylinder of radius 0.15 m and length 1.2 m, chosen to model two-dimensional probe-induced flow distortion in the limit where the scale of the turbulence is very large compared to the scale of the probe. The second sonic anemometer measured the undistorted flow. The measured flow-distortion effects on the Reynolds shearing stress and the variances of streamwise and vertical velocity agree well with the theory.
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  • 23
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    Boundary layer meteorology 92 (1999), S. 37-63 
    ISSN: 1573-1472
    Keywords: Energy balance ; Glacier ; Katabatic flow ; Stable boundary layer ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Turbulence measurements performed in a stable boundary layer over the sloping ice surface of the Vatnajökull in Iceland are described. The boundary layer, in which katabatic forces are stronger than the large-scale forces, has a structure that closely resembles that of a stable boundary layer overlying a flat land surface, although there are some important differences. In order to compare the two situations the set-up of the instruments on an ice cap in Iceland was reproduced on a flat grass surface at Cabauw, the Netherlands. Wind speed and temperature gradients were calculated and combined with flux measurements made with a sonic anemometer in order to obtain the local stability functions φm and φh as a function of the local stability parameter z/L. Unlike the situation at Cabauw, where φm was linear as a function of z/L, in the katabatically forced boundary layer, the dependence of φm on stability was found to be non-linear and related to the height of the wind maximum. Thermal stratification and the depth of the stable boundary layer however seem to be rather similar under these two different forcing conditions. Furthermore, measurements on the ice were used to construct the energy balance. These showed good agreement between observed melt and components contributing to the energy balance: net radiation (supplying 55% of the energy), sensible heat flux (30%) and latent heat flux (15%). Local sources and sinks in the turbulent kinetic energy budget are summed and indicate a reasonable balance in near-neutral conditions but not in more stable situations. The standard deviation of the velocity fluctuations σu, σv, and σw, can be scaled satisfactorily with the local friction velocity u* and the standard deviation of the temperature fluctuation σθ with the local temperature scale θ*.
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    Boundary layer meteorology 92 (1999), S. 165-183 
    ISSN: 1573-1472
    Keywords: Coherent structures ; Turbulence ; Surface layer
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Multi-level turbulent wind data from the Risø Air-Sea Experiments (RASEX) were used to examine the structure of large-scale motions in the marine atmospheric surface layer. The quadrant technique was used to identify flux events (ejections/sweeps). Ejections, which appear to occur in groups, are seen to occur first at the upper level, moving successively to lower levels with small time delays. A strong correlation between events at different heights suggests that they may all be part of a single large structure. Cross-correlation between velocity signals was used to estimate orientation of the structure using Taylor's hypothesis. The inclination of this structure is shallow (≃ 15°) near the surface and increases with height. Spatial representations of the fluctuating wind vectors show a structure that is strikingly similar to conceptual models of transverse vortices and shear layers seen in laboratory flows and direct numerical simulation (DNS) of low Reynolds number flows. Spatial visualization of velocity fluctuations during other time periods and conditions clearly shows the existence of shear layers, transverse vortices, plumes, and downdrafts of various sizes and strengths. A quantitative analysis shows an increase in the frequency of shear related events with increasing wind speed.
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    ISSN: 1573-1472
    Keywords: Closure models ; Drizzle ; Entrainment ; Large Eddy Simulation ; Observations ; Stratocumulus ; Turbulence
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    Topics: Geosciences , Physics
    Notes: Abstract As part of the EUropean Cloud REsolving Modelling (EUCREM) model intercomparison project we compared the properties and development of stratocumulus as revealed by actual observations and as derived from two types of models, namely three-dimensional Large Eddy Simulations (LES) and one-dimensional Single Column Models (SCMs). The turbulence, microphysical and radiation properties were obtained from observations made in solid stratocumulus during the third flight of the first 'Lagrangian' experiment of the Atlantic Stratocumulus Transition Experiment (ASTEX). The goal of the intercomparison was to study the turbulence and microphysical properties of a stratocumulus layer with specified initial and boundary conditions. The LES models predict an entrainment velocity which is significantly larger than estimated from observations. Because the observed value contains a large experimental uncertainty no definitive conclusions can be drawn from this. The LES modelled buoyancy flux agrees rather well with the observed values, which indicates that the intensity of the convection is modelled correctly. From LES it was concluded that the inclusion of drizzle had a small influence (about 10%) on the buoyancy flux. All SCMs predict a solid stratocumulus layer with the correct liquid water profile. However, the buoyancy flux profile is poorly represented in these models. From the comparison with observations it is clear that there is considerable uncertainty in the parametrization of drizzle in both SCM and LES.
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    Studia geophysica et geodaetica 42 (1998), S. 382-390 
    ISSN: 1573-1626
    Keywords: Magnetohydrodynamics (MHD) ; Turbulence ; Magnetic fields ; Galaxies
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences , Physics
    Notes: Abstract We present simulations of the 3D nonlinear induction equation in order to investigate the temporal evolution of large-scale magnetic fields in spiral galaxies. Our model includes differential rotation, ambipolar diffusion and, based on small-scale turbulence, eddy diffusivity and the tensorial α-effect with magnetic feedback. The nonaxisymmetric spiral pattern and – if considered – the vertical stratification of the galaxy are represented in its density and turbulence profile. Neglecting vertical stratification the lifetime and geometry of an initial magnetic field depend on the correlation time of interstellar turbulence τ corr . Short correlation times increase the lifetime of the initial magnetic field, but the field is rapidly wound up. Its pitch-angles develop to zero. The magnetic field has disappeared after at most 1 to 1.5 Gyr. A resonance like phenomenon is found by tuning the pattern velocity of the galactic spiral. The simulations then show an exceptional amplification of the magnetic field in the case that the pattern speed and a magnetic drift velocity have similar values. Considering a vertical stratification we achieve sufficiently long living grand-designed magnetic fields excited by dynamo action. The behaviour and geometry of the resulting field is again significantly influenced by the correlation time τ corr . Small values of τ corr lead to axisymmetric fields with small pitch-angles and field-concentration between the spiral arms. Increasing the correlation time the solutions show larger pitch-angles; and depending on very large correlation times the galactic dynamo rather generates fields clearly within the spiral arms and having a bisymmetric structure.
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    Boundary layer meteorology 88 (1998), S. 211-237 
    ISSN: 1573-1472
    Keywords: Aircraft measurements ; Compositing ; Rayleigh-Bénard convection ; Spectral energetics ; Thermals ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract A turbulence data set collected by the research aircraft Hercules and Falcon in the planetary boundary layer (PBL) over the North Sea during Rayleigh-Bénard convection (RBC) is analysed. Altogether nearly three hundred cell passages at different levels and in two different flight directions were sampled. The convective boundary-layer height (H) was about 1 km, and the RBC cells had a diameter D of roughly 2–3 km, resulting in an aspect ratio A = D/H ≈ 2–3. This value is also found in the case of RBC in laboratory-scale flows, whereas most of the recent PBL experimental work reports convection PBL rolls with A ≈ 3 and mesoscale cellular convection (MCC) with A ≈ 10–40 over the oceans. The large number of RBC cell passages made it possible to composite their average structure. Due to the more complex three-dimensional structure and the importance of thermals to the RBC dynamics, spectral, temporal and spatial decompositions and model calculations were necessary to illuminate structure, dynamics, energetics and organisation. The final impression is that the structure of RBC in the PBL is given by a honeycomb-like arrangement of short-lived mixed-layer thermals with more passive downward motions in between. The regularity of the Cu-cloud cover results partly from the more stationary flow in the cloud-free cell centres. On the other hand it is shown that active as well as inactive clouds contribute to the cloud cover. Thus, the PBL flow and the cloud cover are decoupled, at least temporarily and locally. Due to sparse observational and measured information about RBC occurrence and structure in the PBL, additional material was gathered, resulting in the impression that RBC is one additional realised mode of organised convection in the PBL, as has already been clarified for PBL rolls and MCC by recent investigations.
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    ISSN: 1573-1472
    Keywords: Heterodyne Doppler lidar ; Organized large eddies ; Planetary boundary laye ; Turbulence
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    Topics: Geosciences , Physics
    Notes: Abstract In an experiment investigating the planetary boundary layer (PBL) wind and temperature fields, and PBL inversion height recorded by various instruments, the results reveal the presence of organized large eddies (OLE) or rolls. The measurements by lidars, anemometers, soundings and sodar gave an overview of the characteristics of the rolls and sources of energy production that maintain them. The experimental results obtained on two consecutive days are compared to model outputs. The agreement is excellent, showing that thermal stratification and wind shear are important factors in the structure and dynamics of OLE. A heterodyne Doppler lidar (HDL) is shown to be a useful tool in the study of OLE.
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    Boundary layer meteorology 89 (1998), S. 47-74 
    ISSN: 1573-1472
    Keywords: Canopy closure model ; Pine forest ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Simultaneous triaxial sonic anemometer velocity measurements vertically arrayed at six levels within and above a uniform pine forest were used to examine two parameterization schemes for the triple-velocity correlation tensor employed in higher-order closure models. These parameterizations are the gradient-diffusion approximation typically used in second-order closure models, and the full budget for the triple-velocity correlation tensor typically employed in third-order closure models. Both second- and third-order closure models failed to reproduce the measured profiles of the triple-velocity correlation within and above the canopy. However, the Reynolds stress tensor profiles (including velocity variances) deviated greatly from the measurements only within the lower levels of the canopy. It is shown that the Reynolds stresses are most sensitive to the parameterization of the triple-velocity correlation in these lower canopy regions where local turbulent production is negligible and turbulence is mainly sustained by the flux transport term. The failure of the third-order closure model to reproduce the measured third moments in the upper layers of the canopy-top contradicts conclusions from a previous study over shorter vegetation but agrees with another study for a deciduous forest. Whether the third-order closure model failure is due to the zero-fourth-cumulant closure approximation is therefore considered. Comparisons between measured and predicted quadruple velocity correlations suggest that the zero-fourth-cumulant approximation is valid close to the canopy-atmosphere in agreement with recent experiments.
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    ISSN: 1573-1472
    Keywords: Atmospheric surface layer ; Longitudinal velocity fluctuations ; Multifractals ; Spectra ; Statistical analysis ; Turbulence
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    Topics: Geosciences , Physics
    Notes: Abstract The multiscaling statistics of atmospheric surface-layer winds at low wavenumbers above farmland and in the lee of a mountain range were examined using a hot-wire and lightweight cup anemometer. It was found that the horizontal velocity spectra could be broken into high and low-wavenumber regimes according to the parameters given by this analysis. The low-wavenumber end of the spectrum possessed a spectral slope parameter that varied between values of 0.8 and 1.35 at the farmland site during the period of the experiment, and the high-wavenumber end – corresponding to the inertial range – possessed a spectral slope slightly greater than -5/3. The larger values for this parameter for the low-wavenumber end appeared to coincide with unstable conditions. In the lee of the mountain range, the low-wavenumber spectral slope parameter was larger still, at 1.45. The low-wavenumber signals over farmland were much less intermittent than inertial-range signals, but in the lee of the mountain range the intermittency increased. From this analysis, it was shown that the statistical properties of the recorded wind signal could be reproduced using a bounded random multiplicative cascade. The model was successfully used to simulate the wind velocity field directly, rather than simulating the energy dissipation field. Since the spectral slope parameter for low wavenumbers appeared to be a function of atmospheric stability, the method presented is a simple way of generating wind signals characteristic of a variety of atmospheric conditions.
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    Boundary layer meteorology 92 (1999), S. 99-121 
    ISSN: 1573-1472
    Keywords: Displacement height ; Ice surface roughness ; Katabatic flow ; Stable boundary layer ; Turbulence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Wind profile and eddy-correlation data obtained at two sites on a melting glacier surface in Iceland during the summer of 1996 are presented. Throughout the experiment the surface roughness increased rapidly from smooth to very rough, with the largest roughness element height obtained being about 1.7 m. In a layer close to the rough surface we find that the wind speed profiles were disturbed showing horizontal inhomogeneities as in a roughness sublayer. Its height was approximately two times the height of the main roughness elements (h) at both sites throughout the experiment. From the wind profiles and eddy-correlation data we calculated corrections for the displaced zero plane as a function of time and compared these with results obtained from a drag partitioning model. In general, the agreement was reasonable considering the ranges of uncertainty but the results indicate that the increasing horizontal anisotropy of the surface probably limits the use of the model. The values obtained for the roughness lengths are in good agreement with those calculated from a simple linear model, i.e., z0/h = 0.5λ with λ the frontal area index. Above the roughness sublayer the wind profiles, normalised standard deviations of wind speed, and the balance of the turbulence kinetic energy budget behaved as over an ideal homogeneous surface thereby confirming similarity of the flow.
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    Boundary layer meteorology 81 (1996), S. 399-410 
    ISSN: 1573-1472
    Keywords: Turbulence ; Coherence ; Taylor’s hypothesis ; Surface layer
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    Topics: Geosciences , Physics
    Notes: Abstract Experimentally obtained time coherence has traditionally been interpreted as streamwise one-dimensional spatial coherence through Taylor’s hypothesis. We calculate corrections to the highwavenumber part of the coherence to account for the errors caused by the deviation from Taylor’s hypothesis in high-intensity turbulent flows. The small-scale turbulence is assumed to be frozen and convected by a fluctuating convection velocity. Both Lumley’s two-term approximation and the Gaussian approximation are used in the calculations. In general, we find that the coherence for crossstream separations is significantly overestimated by the direct use of Taylor’s hypothesis, the error increasing with wavenumber; that for streamwise separations is underestimated. The analyses are compared with cross-stream coherence measurements in the atmospheric surface layer. Our results indicate that predictions from Lumley’s approximation yield better agreement with experimental data for cross-stream separations than those from the Gaussian model. Our study suggests that reliable measurement of two-point spatial coherence can be achieved only for scales not too small compared to the sensor separation.
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    Boundary layer meteorology 83 (1997), S. 43-73 
    ISSN: 1573-1472
    Keywords: Model evaluation ; Mesoscale ; Turbulence ; Dispersion ; Convective boundary layer ; Complex terrain
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    Topics: Geosciences , Physics
    Notes: Abstract A prognostic three-dimensional mesoscale model has been developed andused in one- and two-dimensional modes to evaluate ten local turbulenceclosure schemes. The schemes ranged from first-order to the two-equationprognostic schemes. Predictions by the models were compared for aone-dimensional convective boundary layer using mixed layer scaling andmeasurements to interpret the results. Two-dimensional simulations were alsoperformed for a sea-breeze flow and for flow over a hill. The results showedthat for all of the models considered, minor differences were produced in themean meteorological fields and in the vertical scalar fluxes, but majordifferences were apparent in the velocity variances and dissipation rate.Predicted tracer concentrations were very sensitive to the turbulence modelformulation for dispersion from a point source in the convective boundarylayer, particularly for the prediction of maximum concentrations. Predictedtracer concentrations from a surface volume source for the two-dimensionalsimulations were similar for all models, although the degree of mixing in themorning growth period produced some differences. Generally, good results forthe mean meteorological fields can be obtained with first-order schemes, evenif they underpredict the magnitude of turbulence in the convective boundarylayer, and reasonable tracer concentrations can also be obtained with thesemodels provided near-source effects are not important. The two-equationprognostic models performed best for the prediction of turbulence in theconvective boundary layer.
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    Boundary layer meteorology 84 (1997), S. 1-22 
    ISSN: 1573-1472
    Keywords: Large-eddy simulation ; Turbulence ; Non-local closure ; Convective boundary layer
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    Topics: Geosciences , Physics
    Notes: Abstract Recently Frech and Mahrt proposed a closure scheme which includes alarge-scale stress term to represent the effects of non-local momentummixing in the convective boundary layer. Here large-eddy simulation (LES)datasets are used to evaluate the performance of this scheme across a rangeof stabilities between neutral and highly convective conditions, and as afunction of baroclinity. Generally the inclusion of the non-local term inthe closure model leads to results in better agreement with LES, althoughsome modifications to the model formulation are suggested.
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    Boundary layer meteorology 85 (1997), S. 35-52 
    ISSN: 1573-1472
    Keywords: Turbulence ; Atmospheric convective boundary layer ; Correlation function
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    Topics: Geosciences , Physics
    Notes: Abstract A three-dimensional model for correlation functions and spectra in theatmospheric, convective boundary layer (CBL) is presented. The modelincludes vertical inhomogeneities introduced by eddy-blocking at the ground.By assuming the disturbance to the turbulent flow resulting from the groundblocking is irrotational, an equation is developed which allows one to writethe inhomogeneous, two-dimensional (2D) cross spectra for the blocked flowin terms of the 2D cross spectra for a homogeneous flow. VonKármán's energy spectrum then is used to determine thehomogeneous, 2D cross spectra. Although there are only two adjustableparameters in the model, the variance and a length scale, the model is shownto agree quite well with a diversity of previous results for the CBL.
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    Boundary layer meteorology 89 (1998), S. 141-159 
    ISSN: 1573-1472
    Keywords: Radiation ; Stable conditions ; Turbulence
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    Topics: Geosciences , Physics
    Notes: Abstract The interaction between longwave radiation and temperature fluctuations plays a role in the dissipation of temperature variance. This interaction is most easily described by spectral models of atmospheric turbulence and a spectral radiative dissipation function which gives the intensity of the damping at each radiative wavelength λ and wavenumber k. We have used a Corrsin–Pao closure for the spectral budgets of turbulent kinetic energy and temperature to study the coupling of radiation to turbulence. The spectral radiative dissipation function and a related integral have been fitted by analytical approximations with the correct asymptotic behavior. This resulted in a simple analytical formula for the dimensionless temperature spectrum as a function of Monin-Obukhov stability, and a new dimensionless parameter describing the relative importance of radiation in the temperature spectral budget. The radiative effects both on the temperature spectrum and on the dimensionless temperature variance can then be calculated. Based on typical values of the radiative dimensionless parameters for the surface layer, we conclude that radiative dissipation is probably negligible there.
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    Boundary layer meteorology 89 (1998), S. 109-140 
    ISSN: 1573-1472
    Keywords: BOREAS ; Eddy correlation ; Eddy covariance ; Turbulence ; Understory
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    Topics: Geosciences , Physics
    Notes: Abstract Turbulent flux measurements both above and beneath the canopy of a boreal aspen forest are described. Velocity skewness showed that, beneath the aspen canopy, turbulence was dominated by intermittent, downward penetrating gusts. Eulerian horizontal length scales calculated from integration of the autocorrelation function or spectral peaks were 9.0 and 1.4 times the mean aspen height of 21.5 m respectively. Above-canopy power spectral slopes for all velocity components followed the -2/3 power law, whereas beneath-canopy slopes were closer to -1 and showed a spectral short cut in the horizontal and vertical components. Cospectral patterns were similar both above and beneath the canopy. The Monin–Obukhov similarity function for the vertical wind velocity variance was a well-defined function of atmospheric stability, both above and beneath the canopy. Nocturnal flux underestimation and departures of this similarity function from that expected from Monin–Obukhov theory were a function of friction velocity. Energy balance closure greater than 80% was achieved at friction velocities greater than 0.30 and 0.10 m s-1, above and below the aspen canopy, respectively. Recalculating the latent heat flux using various averaging periods revealed a minimum of 15 min were required to capture 90% of the 30-min flux. Linear detrending reduced the flux at shorter averaging periods compared to block averaging. Lack of energy balance closure and erratic flux behaviour led to the recalculation of the latent and sensible heat fluxes using the ratio of net radiation to the sum of the energy balance terms.
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    Boundary layer meteorology 90 (1999), S. 397-421 
    ISSN: 1573-1472
    Keywords: Gravity waves ; Planetary boundary layer ; Turbulence ; Wind structure
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    Topics: Geosciences , Physics
    Notes: Abstract The stably-stratified planetary boundary layer contains small-vertical-scale, step-like structures, waves on a multitude of scales, large horizontal eddies and small-scale turbulence, all of which constantly interact with, and modify, one another. Current knowledge of how the various components act in the vicinity of the step-like structures is surveyed. It is concluded that packets of internal waves are the main conduit for interaction within and across the boundary layer, and low-intensity critical-level absorption at the fringes of their spectrum probably maintains the step-like structures. Further investigation of the processes requires intensive observations of the four-dimensional structure of the region, but such an investigation will need a new generation of high-resolution sensing systems.
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    Boundary layer meteorology 92 (1999), S. 263-291 
    ISSN: 1573-1472
    Keywords: Convective adjustment ; Turbulence ; Mixing ; Nonlocal mixing ; Parameterization ; Numerical weather prediction
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    Topics: Geosciences , Physics
    Notes: Abstract A nonlocal turbulent mixing parameterization is introduced in this study and denoted by the acronym NTAC, which stands for Nonlocal parameterization of Turbulent mixing using convective Adjustment Concepts. NTAC uses the average value of quantities in the turbulent domain in much the same way that local convective adjustment schemes use the average potential temperature. Averages are determined in the region with non-convective turbulence using information from the two end layers (denoted by TLA, Two Layer Average), while all layers contribute to the average in regions with convective turbulence (denoted by CLA, Convective Layer Average). The NTAC parameterization estimates the mixing percentage and uses this percentage as a mixing coefficient. These percentages are determined from a simplified turbulent kinetic energy equation. The scheme is versatile, conservative, and when programmed efficiently the proposed parameterization is a computationally acceptable nonlocal procedure that can be used in many existing numerical weather prediction forecast models. Numerical weather forecast model simulations using the NTAC parameterization and traditional K-theory are compared against radiosonde data. The accuracy of the proposed NTAC parameterization is found to be competitive with K theory. The greatest improvement of the NTAC over K-theory occurs during the daytime and early nighttime hours when (dry) convective activity is high. Also, areal cloud coverage is increased by the NTAC parameterization. Our findings show that the greatest nonlocal vertical mixing occurs between the layer nearest the earth's surface and the remaining layers making up the planetary boundary layer.
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    Boundary layer meteorology 83 (1997), S. 117-137 
    ISSN: 1573-1472
    Keywords: Reynolds averaging ; Turbulence ; Time series ; Cospectra ; Sampling error
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    Topics: Geosciences , Physics
    Notes: Abstract Geophysical variables are orthogonally decomposed by averaging timeseries using different averaging lengths, referred to as a (Haar)multiresolution decomposition. This simple and economic decomposition isassociated with cospectra that formally satisfy Reynolds averaging rules foreach averaging length. The multiresolution decomposition provides a naturalestimate of the random error in estimating a mean turbulent flux. The Fourierand multiresolution decompositions are compared using aircraft data fromBOREAS.
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    ISSN: 1573-1472
    Keywords: Turbulence ; Canopies ; Temperature ramps ; Structure functions
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    Topics: Geosciences , Physics
    Notes: Abstract Air temperature time series within and above canopies reveal ramp patternsassociated with coherent eddies that are responsible for most of thevertical transport of sensible heat. Van Atta used a simple step-changeramp model to analyse the coherent part of air temperature structurefunctions. However, his ocean data, and our own measurements for aDouglas-fir forest, straw mulch, and bare soil, reveal that even withoutlinearization his model cannot account for the observed decrease of thecubic structure function for small time lag. We found that a ramp model inwhich the rapid change at the end of the ramp occurs in a finite microfronttime can describe this decrease very well, and predict at least relativemagnitudes of microfront times between different surfaces. Averagerecurrence time for ramps, determined by analysis of the cubic structurefunction with the new ramp model, agreed well with values determined usingthe Mexican Hat wavelet transform, except at lower levels within theforest. Ramp frequency above the forest and mulch scaled very well withwind speed at the canopy top divided by canopy height. Within the forest,ramp frequency did not vary systematically with height. This is inaccordance with the idea that large-scale canopy turbulence is mostlygenerated by instability of the mean canopy wind profile, similar to aplane mixing layer. The straw mulch and bare soil experiments uniquelyextend measurements of temperature structure functions and ramp frequencyto the smallest scales possible in the field.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 103-119 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The spontaneous shear band formation in the biaxial test on dry sand samples with constant cell pressure is treated as a bifurcation problem. The constitutive response of sand is described in terms of mobilized friction and dilatancy. Dilatancy is looked upon as an internal constraint and the hardening rule is expressed in terms of an adequate dimensionless stress measure. Owing to fail of normality in sand, localization always occurs in the hardening regime. The theoretical solution of the shear band inclination is a geometrical mean of the classical Coulomb and Roscoe solutions and is in good agreement with the experimental data. The incipient shear modulus is proportional to the stress level and can be estimated to be also proportional to these cant modulus.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 175-184 
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    Keywords: Engineering ; Engineering General
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    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 291-292 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 293-311 
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    Keywords: Engineering ; Engineering General
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    Notes: Hysteretic and viscous material damping are compared in the context of soils. Popular assumptions about damping are shown to lead to different results for the rocking mode of surface foundations at low frequency.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 389-389 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 57-78 
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    Keywords: Engineering ; Engineering General
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    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The trap-door problem with dry sand is treated in a statical analysis based upon model test kinematics. Integration of the equilibrium conditions along horizontal slices and introducing the mean value for the vertical stresses yields a differential equation for the trap-door force. Concerning the constitutive response of sand a statical model of a moving shear band is proposed as an internal boundary. Solutions for the trap-door force for the active and passive modes and for the ultimate and residual states are discussed.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. i 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 333-359 
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    Keywords: Engineering ; Engineering General
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    Notes: The analysis of the stability of slopes using limiting equilibrium considerations necessitates the determination of the critical slip surface which yields the minimal factor of safety. The numerous methods currently available for slope stability analysis provide a procedure for assigning a factor of safety to a given slip surface, but do not consider the problem of identifying the critical conditions.This paper presents an effective minimization procedure based on dynamic programming by which the minimal factor of safety, and the corresponding surface, are determined simultaneously. This procedure SSDP (Slope Stability by Dynamic Programming), couples the minimization scheme with Spencer's method of slope stability analysis. It may be applied to slopes of any geometry, layering, pore pressure and external load distributions. No arbitrary restrictions are placed on the shape of the slip surfaces, and the analysis satisfies all equilibrium equations.Application of the procedure to slope stability problems reported in the literature shows that for a given slip surface the procedure yields factors of safety which are almost identical to those reported, but in every case a more critical slip surface, with a lower factor of safety, may be found.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 361-375 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    Notes: A new concept based on the use of a function expressed as a (complete) polynomial expansion in terms of the three invariants of the stress tensor is proposed for deriving yield, failure and plastic potential functions for use in plasticity based constitutive laws. A mathematical interpretation and physical meaning of the proposed concept are provided by using the idea of the singular nature of constiutive matrices in incremental hypoelastic laws. It is suggested that the proposed function and (polynomial) forms of material moduli can be synonymous. A number of specialized forms of the general function are adopted and their values at failure from advanced three-dimensional tests for a number of (geological) media are evaluated. The results indicate the possibility that there exist invariant numbers associated with the functions(s) that may apply to a wide range of materials. Some ideas on implementation of the proposed concept are also presented.
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981), S. 139-163 
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    Notes: A novel finite element method has been proposed in this paper for the solution of seepage problems economically and accurately. In this method the governing equation and the prescribed boundary conditions are transformed so that they refer to a suitable logarithmically condensed ‘image’ space; the physical problem domain is also mapped into the image space. The transformed equation is then solved in the image space using standard finite elements, subject to the transformed boundary conditions. Because physical space is logarithmically condensed in the image space, the proposed method is capable of dealing with large or very large aspect ratio seepage problems economically and accurately.The validity of the method has been demonstrated by means of a number of examples including anisotropy and non-linearity. In all cases an excellent degree of accuracy was achieved, efficiently and economically.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 77-94 
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    Notes: It is commonly accepted that the mechanical behaviour of granular masses is strongly affected by their microstructure, namely the relative arrangement of voids and particles, i.e. the granular fabric. Therefore, parameters which characterize the granular fabric are of paramount importance in a fundamental description of the overall macroscopic stresses and deformation measures. In this paper several measures of granular fabric are introduced for a random assembly of spherical granules, using a statistical approach. In particular, a second-order symmetric tensor, Fij, emerges from this consideration, which seems to be of fundamental importance for the description of fabric, and which is closely related to the distribution of the contact normals in the assembly. The relation between fabric measures presented here and those discussed by other investigators is also discussed.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 141-145 
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    Notes: A mapping finite element method is proposed for the solution of elastic problems in two-dimensions. This method, based on the logarithmic condensation of physical space, is found to give significantly greater accuracy than when the problem is solved in the physical plane using the standard FEM. Logarithmic condensation of space also permits the solution of large aspect-ratio problems of this type, accurately and economically.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. i 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 151-171 
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    Notes: A method for the analysis of the consolidation of a horizontally layered soil under plane conditions is developed. The method depends upon the transformation of the governing equations by a Fourier trasform. This transformation has the effect of reducing the partial differential equations of consolidation to ordinary differential equations. The ordinary differential equations are then solved using a finite layer or finite difference approach. Once the solution in the transformed plane has been found, the actual solution is synthesized by Fourier inversion. The method leads to a considerable reduction in the amount of core storage necessary for solution and enables the solution of quite significant problems to be obtained on a mini-computer.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 233-254 
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    Keywords: Engineering ; Engineering General
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    Notes: A new one-dimensional model for penetration analysis of a rigid projectile into a soil target is presented. The soil medium is represented by a set of discs of constant thickness, responding in the radial direction under plain strain regime. When penetration through a typical disc occurs, the projectile displaces soil material and a radial plastic shock wave propagates in the disc. The interaction pressure between the projectile and soil material is compatible with the motion of the contact boundary, between them. The instantaneous resistive force is obtained by summation of the contributions of all the discs which are in contact with the nose surface of the projectile. Soil is considered as a ‘floating’ ideally locking material, in which the locking volumetric strain is adjusted to the physical stress-strain properties of the soil material. Friction between projectile and soil is assumed to be negligible. Comparison is made with both twodimensional computer program results and experimental data, and very good agreement is observed. Comparison with other analytical methods reveals that the present model most closely resembles existing experimental results and permits further analysis of the problem as predictions of target response and of stress distribution on the projectile nose. The calculations require very small amounts of computer time. Analysis with the present model yields an efficient and comprehensive means to analyse penetration and perform parameter analysis.
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    International Journal for Numerical and Analytical Methods in Geomechanics 4 (1980), S. 377-387 
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    Notes: A new and simple concept based on the idea of correcting for non-associative characteristics of (geologic) media is presented. A special form of the concept is adopted and introduced in a critical state plasticity model. An example problem of behaviour of a soil tested under triaxial conditions is included. The concept can permit a simplified treatment of non-associativeness and under certain assumptions can allow use of existing formulations of plasticity by maintaining symmetry of the associated matrices.
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    International Journal for Numerical and Analytical Methods in Geomechanics 5 (1981) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 187-196 
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    Notes: Localization of deformation in elastic-plastic solids subject to plane strain deformation are investigated numerically. It is shown that the localization may be captured accurately in finite element models by employing (1) the elastic-plastic material stiffness to form the global stiffness, (2) in the case of symmetrical configurations, an imperfection in the form of a weak element, and (3) in the case of incompressible materials, a reduced selective integration scheme which alleviates mesh ‘locking’. Accuracy of the technique is demonstrated by applying it to analyse the classical punch and slope stability problems. Its versatility is illustrated by applying it to analyse finite deformation problems and shear bands formations in associative and non-associative elastic-plastic solids.
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 95-108 
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    Notes: The notion of overall macroscopic stress in granular masses is examined from a fundamental point of view by a statistical consideration of the contact forces that are transmitted by the contacting granules at the microscale. This examination leads in a natural way to relations between the macroscopic stress and the resulting granular fabric. The overall stresses are expressed in terms of the contact forces in two different but complementary ways: (1) by a statistical averaging over the sample volume of contact forces and “branches” which are vectors connecting the centroids of two contacting granules; and (2) by defining the overall tractions transmitted across an interior imagined plane as the sum of the contact forces which represent the mechanical effect of granules on one side of a unit area of this plane, upon those on the other side. Conditions under which the two representations of overall stresses are equivalent, are examined in detail. In addition, explicit results are given, which, define stresses in terms of the fabric and other microstructural characteristics of the granular mass.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 306-308 
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    International Journal for Numerical and Analytical Methods in Geomechanics 6 (1982), S. 195-209 
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    Notes: During the last ten years the Calculus of variations technique has been applied to solve the problem of stability of slopes. All published methods are essentially based on the attainment of a functional and the search for its absolute minimum or maximum by vanishing its first variation.Obviously this statement of the problem is valid only if such a minimum or maximum exists and can be obtained by making the first variation of the functional equal to zero. So, these implicit hypotheses must be checked.This work analyses from this point of view the validity of the methods proposed by ‘Baker and Garber’, ‘Chen’ and ‘Castillo and Revilla’, and demonstrates that the first two methods are incorrectly stated while the third one is correct at least in the case of a frictionless soil.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 513-517 
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    Notes: A method is devised for measuring soil thermal diffusivity in situ. It is based on direct experimental simulation of the finite difference approximation to the one-dimensional heat conduction equation.The method does not require the soil to be homogeneous except between the three thermometers that are used, at depths z + d, z and z - d. Nor need the energy input curve be sinusoidal. However, it must be fairly smooth for the finite difference approximation to be accurate.Experimental results for London Clay are presented, obtained using thermometers at depths of 1, 6 and 11 cm to give a mean thermal diffusivity of 0.0074 cm2/s at a depth of 6 cm. This value is consistent with other estimates of diffusivity for clay soils.The method is capable of automation, and should be suitable for use on engineering sites, at low cost.The method is capable of generalization to other linear diffusion equations containing one independent parameter. The same limitation also applies to its application to constitutive or geometrical non-linear one dimensional diffusion equations, and each equation requires individual study to assess feasibility of use of the method.The method in effect uses the usual finite difference approximation, not to prepare a numerical solution, but to design an experiment carried out essentially within the finite difference ‘molecule’. The measured parameter of the diffusion equation is the usable product of the method.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 519-529 
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    Keywords: Engineering ; Engineering General
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    Notes: The pressure versus settlement response is highly non-linear for soils, in general. In the present study, a cubic equation of the type p = K1w - K2w3 is suggested to incorporate the non-linear behaviour. A trapezoidal footing with constant depth resting on a subgrade having non-linear response is analysed. The resulting fourth order non-linear differential equation with variable coefficients is solved by using the Galerkin technique and beam characteristic functions are employed to obtain faster convergence. The results are presented in the form of non-dimensional charts for valid ranges of footings and soil parameters.
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    International Journal for Numerical and Analytical Methods in Geomechanics 8 (1984), S. 589-604 
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    Notes: The analysis of mechanisms which could control the growth of fractures in non-homogeneous regions is of paramount importance. One such mechanism is the behavior of the fracture as it reaches a frictional interface; coupled with this is the question of re-initiation, e.g. whether a fracture can be contained within the region of initiation. Though the problems of slippage have been dealt with by other investigators, the present paper gives a more comprehensive picture and detailed treatment: effects of various frictional models at an interface are considered for a crack which intersects it at any angle; specialization then allows comparison with existing results in the literature.The problem of re-initiation, after slippage has occurred at a frictional interface, is also considered, using two different models. First, by introducing microcracks in the adjacent stratum and looking at the effects on propagation criteria and, secondly, by examining the actual distribution of the stress tangential to the slip surface; detailed computations are performed and a simple criterion for re-initiation is given, relating the re-initiation stress dominantly to the confining stress on the interface.
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    International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985), S. 15-27 
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    Keywords: Engineering ; Engineering General
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    Notes: On the basis of the two-dimensional theory of elasticity, the theoretical analysis of a vertical, fluid-filled crack intersecting and oblique joint has been made for the extraction of geothermal heat from hot, dry rock masses, where the opening of the joint near a point of intersection and the frictional resistance against slips along the joint are taken into account. The stress intensity factors are evaluated for discussing crack kinking at the upper joint tip, and the sufficient conditions on theinclination of the joint and on the length between the upper joint tip and the point of intersection are obtained for keeping a fluid-filled crack stable just beneath a joint. It is also shown that the volume of the stable reservoir created by using a joint is much larger than that of a fluidfilled crack in a jointless rock mass, even if the joint is oblique and is opened up by the fluid pressure.
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    International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985), S. 91-99 
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    Notes: The plate loading test is performed in order to determine the deformation modulus of a rock mass in situ. In the standard execution of this test the loading is applied perpendicular to the rock surface. The displacements are measured on the axis of symmetry, since for an isotropic material with linear deformation characteristics exact formulae are known which are valid at this location. For horizontal strata this presents no problem as it is easy to provide loading in a vertical direction. When the rock strata are dipping it is imprectical to use nonvertical load and it is then necessary to calculate the modulus from the displacements in a non-axisymmetrical arrangement. Using the well-known method of the Taylor series approximate formulae are derved which are sufficiently accurate for all practical cases of sloping rock.
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    International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985), S. 161-172 
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    Notes: A coupling scheme for boundary and finite elements using a joint element is proposed. The scheme is based on the finite element discretization (i.e. the equivalent FE procedure). Footing problems founded on multiple layers are solved. Furthermore, the scheme is extended to a non-linear analysis.
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 117-127 
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    Notes: A coupled finite element-rigid block model for the transient analysis of caverns in jointed media is presented. This coupling permits the modelling of lined openings in a jointed rock mass as well as the propagation of stress waves to the cavern. Both the finite element and the rigid block algorithms employ explicit time integration; an efficient, stable scheme is developed for coupling the two algorithms. Two numerical examples are given: one is a simple validation, the second is a representation of a lined cavern in a sparsely jointed medium.
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    International Journal for Numerical and Analytical Methods in Geomechanics 10 (1986), S. 111-112 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983) 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 385-393 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. ii 
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    International Journal for Numerical and Analytical Methods in Geomechanics 7 (1983), S. 457-468 
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    Notes: This paper sets forth the theoretical background and basic numerical expressions for the incorporation of elastic-plastic constitutive equations for ductile rock into a finite element computer code. The derivation of an expression for the total strain rate is performed both for a total stress formulation and for a formulation that employs the concept of effective stress for inelastic behaviour. Specific expressions for the incremental strain rate are presented for the case of a porous material having a quadratic initial yield surface and observing the associated flow rule with a special hardening law for subsequent plastic deformation. A final section of the paper summarizes the expressions required to insert the quadratic yield surface model into a finite element code.
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    International Journal for Numerical and Analytical Methods in Geomechanics 10 (1986), S. 367-381 
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    Notes: A method for predicting the maximum mobilized side resistance and unit shaft resistance-displacement curves (load transfer functions) on piles in clay is described. The method was derived using a numerical solution to model pile installation effects and a finite element scheme to model pile loading. Results of three well-documented pile load tests on steel piles were used to develop intermediate steps and final solutions, and the method was verified by comparing predicted results to two other load tests. An expression is proposed to represent load transfer functins for use by practitioners for the design of bridge and other foundations in clay.
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    International Journal for Numerical and Analytical Methods in Geomechanics 10 (1986), S. 431-441 
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    Notes: This paper discusses the kinematic admissibility of axisymmetric velocity fields for the upper bound stability analysis of slopes surrounding cylindrical openings in frictional materials. The governing kinematic equations for two corner regimes of the Mohr-Coulomb yield condition are analysed. Although the equations can be solved by the method of characteristics, the characteristics and the characteristic relations for each regime differ significantly, for the Haar-von Karman regime the characteristics are non-orthogonal and strong discontinuities are admissible, whereas for the other regime the characteristics are orthogonal and strong discontinuities must be excluded. Examples of simple velocity fields and the corresponding stability numbers are, given and compared with the partial collapse mechanisms. The solutions are verified against certain inequalities which must be satisfied for kinematical admissibility of axisymmetric velocity fields.
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    International Journal for Numerical and Analytical Methods in Geomechanics 10 (1986), S. 449-458 
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    Notes: This communication describes an approximate method for generalizing homogeneous, linearly elastic, subgrade type solutions of axial pile response to account for soil creep behaviour. The method is very simple to apply and can be used in conjunction with either analytical or numerical elastic solutions. Exact solutions for limiting cases and finite difference solutions in both space and time are presented to confirm that errors introduced by the approximations are small. Because of the theoretical basis of this approach it is anticipated that method can be used with other pile problems, lateral and axial, for both subgrade adn continuum idealizations. Methods for generalizing the results to more complex conditions such as non-homogeneity or time varying loads are given.
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    International Journal for Numerical and Analytical Methods in Geomechanics 10 (1986), S. 461-482 
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    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 10 (1986) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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    International Journal for Numerical and Analytical Methods in Geomechanics 10 (1986), S. 585-608 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: On the basis of the correspondence principle of visco-elasticity, an application is discussed of the boundary integral equation method to the solution of time-dependent stress analysis problems. The adopted solution technique, in addition to the time-dependent stress and strain distributions, enables the determination of a measure of the error affecting the numerical results. The governing equations for the plane strain visco-elastic problem are derived with reference to a generalized Kelvin model consisting of the series of any number of simple kelvin elements, having both volumetric and deviatoric components. To get some insight into the overall performance of the technique, the results obtained in the solution of some test examples are discussed and compared with those dering from the available closed from solutions.
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    International Journal for Numerical and Analytical Methods in Geomechanics 10 (1986), S. 667-667 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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  • 85
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    International Journal for Numerical and Analytical Methods in Geomechanics 11 (1987), S. 1-15 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A numerical procedure is described for the analysis of vertical deformation of smooth, rigid foundations of arbitrary shape on homogeneous and layered soil media. The contact area at the interface of the foundation and soil medium is approximated by square subdivisions. The response of the system is then obtained from the superposition of the influence of the individual subdivisions. The flexibility influence coefficients are based on equivalent smooth, rigid circular areas with the same contact area as the square subdivisions. For foundations on a homogeneous, isotropic elastic half-space, the flexibility coefficients are given analytically by the integrated forms of the Boussinesq's solution. For a layered soil medium, the flexibility coefficients are determined from an axisymmetric finite element analysis which is essentially two dimensional. Thus, there is no necessity for a full three-dimensional finite element analysis. Comparison with solutions obtained using the integral transform technique for smooth, rigid rectangular foundations on a homogeneous, isotropic elastic half-space shows good agreement. Parametric solutions are presented for the response of rectangular foundations on some ‘typical’ soil profiles. The use of a simplified method to estimate the settlement of rectangular foundations on a layered soil medium by superposing solutions for homogeneous, elastic strata is discussed.
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    International Journal for Numerical and Analytical Methods in Geomechanics 11 (1987), S. 61-77 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The complete solution is presented for the transient effects of pumping fluid from a point sink embedded in a saturated, porous elastic half-space. It is assumed that the medium is homogeneous and isotropic with respect to its elastic properties and homogeneous but anisotropic with respect to the flow of pore fluid. The soil skeleton is modelled as a linear elastic material obeying Hooke's law, while the pore fluid is assumed to be incompressible with its flow governed by Darcy's law. The solution has been evaluated for a particular value of Poisson's ratio of the solid skeleton, i.e. 0.25, and the results have been presented graphically in the form of isochrones of excess pore pressure and surface profile for the half-space. The solutions presented may have application in practical problems such as dewatering operations in compressible soil and rock masses.
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    International Journal for Numerical and Analytical Methods in Geomechanics 11 (1987), S. 115-129 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: To facilitate the practical numerical analysis of tunnel structures by means of the finite element method in the case of viscoplastic properties of the rock mass and viscoelastic properties of the shotcrete, this method is coupled to boundary elements. In this way, the unchanged properties of the boundary element region provide enormous savings in computing time. In order to improve the numerical stability of such calculations, a variable time-step analysis was employed for each time step with an iterative correction method. Characteristic values are obtained from measured values by back-analysis.
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    International Journal for Numerical and Analytical Methods in Geomechanics 11 (1987), S. 143-153 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The heat extraction through a geothermal reservoir on an oblique fault plane in the earth's crust is considered. The fault could be modelled mechanically as a frictional contact interface of two elastic bodies. The heat is recovered by circulating fluid through the reservoir, and then the surface of the reservoir is cooled by the fluid. The analysis is based on the two-dimensional theory of quasi-static thermoelasticity. It is concluded from numerical calculations that a geothermal reservoir can be created on an oblique fault plane, and the opened region, i.e. the fluid-filled region, increases gradually with time during the heat extraction. Also discussed are the effects of the fluid pressure and the coefficient of friction on the behaviour of the reservoir.
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  • 89
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    International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985), S. 49-69 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: In this paper, a general variational principle for the initial boundary value problem of quasi-static thermoelastic consolidation is developed by assuming infinitesimal deformation and an incompressible fluid flowing through a linearly elastic solid. By manipulating the coupling operators, an extended form of the variational pronciple is derved. The associated finite element formulation based on this principle is presented and numerical applications for plane strain thermo-elastic consolidation are revealed.
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    International Journal for Numerical and Analytical Methods in Geomechanics 11 (1987), S. 283-305 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: A finite element, variable mesh analysis of unconfined steady-state seepage problems is presented based on a nonlinear programming algorithm. It is shown that the minimization of an objective function which merely represents a measure of the total flux leaving or entering the mesh at the free surface nodes (except those that belong also to pervious boundaries) does not permit a unique definition of the free surface geometry. This problem, which is apparently related to the numerical instabilities often met when using variable mesh approaches, can be eliminated by adding to the objective function a term representing a sort of overall ‘regularity’ condition for the shape of the free surface. The modified solution procedure turns out to be stable and able to provide meaningful results for practical problems even when rather coarse meshes are adopted.
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    International Journal for Numerical and Analytical Methods in Geomechanics 11 (1987), S. i 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 11 (1987), S. 381-390 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Hydraulic and mechanical properties of rock masses are largely dependent upon the distribution and variation of fracture areas. Consequently, it is essential to develop good models for analysing the spatial geometric characteristics of fracture fields. The latter, however, may be ascertained only by measuring open cuts or boreholes. The most important factor from the analysis of areas is to be able to determine spatial networks. Without an exhaustive and expensive inventory, the classical methods involving measurements of dip and strike do not provide either a correct estimation of fracture orientations in space, or a good estimation of their distribution.At present, automatic analysis of linear traces on large plane areas is used by several authors1,2 and the field strike and dip measurements are applied only for verification purposes. This method of computing spatial networks is especially suitable because of the nature of data so obtained, since it permits various simulations on computed networks. It is based upon classical methods of vector geometry that involve a measurements data matrix and provide a means of solving a double system of equations. Results are the directional spatial fracture densities. The object of this paper is to define the geometric parameters of this problem and the computation method, to present an example and, finally, to conclude with critical comments supported by certain proposals for a variety of applications.
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    International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985), S. 296-296 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985), S. 297-297 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
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    International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985), S. 331-351 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: In this paper the settlement of a rigid foundation supported by a layer of clay which has been stabilized with stone columns is considered. The results of an analytic solution for the settlement, assuming no yield occurs in the clay or columns, have been presented in a previous publication. This solution is now used to develop an interaction analysis which takes account of yielding within the stone columns.This interaction analysis is based on a number of plausible assumptions regarding the behaviour of the clay and columns. In order to check the validity of these assumptions elasto-plastic finite element analyses have been performed and the agreement between the two methods is very good. However, the computational effort required for the finite element analyses is many orders of magnitude greater than that for the interaction analysis.This analysis has been used to generate a number of parametric solutions which provide a basis for estimating the reduction in settlement of the foundation due to the stabilization of the clay.
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    International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985), S. 399-414 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: Stability and bifurcation of plane-strain, undrained, rectilinear deformations on water-saturated granular soil specimens are discussed. The soil, sand or normally consolidated clay, is described by a 2D-flow theory of plasticity for frictional material with non-associated flow rule. Contractant material become unstable (liquefies) at the state of maximum deviatoric stress. For dilatant material the dominant failure mode is shear banding that occurs close to the state of maximum principal effectivestress ratio. The theoretical findings are supported by and are used to explain existing experimental results.
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    International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985), S. 505-505 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
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    International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985) 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
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    International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985), S. 557-571 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The finite element method (FEM) and the boundary element method (BEM) are two well established numerical methods used for the analysis of underground openings. The advantages of both the methods are utilized by adopting FEBEM in which finite elements are coupled with boundary elements. A coupling procedure is presented in this paper. In using FEBEM, the effect of the location of interface boundary between finite element and boundary element regions, effect of Poisson's ratio and effect of stress ratio are discussed. It is shown that Poisson's ratio and stress ratio have significant effect on the accuracy of the results. Different discretization schemes are discussed to study their effect on accuracy and computation time. The use of different material properties in the FE region is presented. A comparative study is made with FEM for all the cases. It is shown that use of FEBEM is more advantageous than FEM.
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    International Journal for Numerical and Analytical Methods in Geomechanics 9 (1985), S. 599-608 
    ISSN: 0363-9061
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Architecture, Civil Engineering, Surveying , Geosciences
    Notes: The current work uses Baiocchi's transformation to obtain heuristically a formulation of the inhomogeneous dam problem. When finite element methods are applied the finite dimensional problem is a variational inequality which may be solved to obtain approximate solutions. The main advantage of the method is that it uses a fixed mesh.The finite dimensional problem is solved by means of succesive overrelaxation with projection. Although the standard convergence theory1 for this method does not apply in this case, because the stiffness matrix is not symmetric, satisfactory and rapid convergence was obtained in all of our examples.Numerical results are given for some examples.
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