ALBERT

Description: Historically, scientists who perform low-level measurements of 14C for age dating, and 3H2O for environmental contamination, have purchased or constructed highly specialized instruments to quantitate low-level radionuclides using a general-purpose liquid-scintillation analyzer (LSA). The LSA uses special time-resolved 3-D spectrum analysis (TR-LSC) to reduce background without substantially affecting sample counting efficiency. This technique, in combination with a special slow fluor scintillating plastic, further reduces the minimal detectable limit for the TR-LSC liquid scintillation counter.

Description: We discuss here the variability, for our laboratory, in counting for radiocarbon dating of replicate measurements of background and secondary modern standard, duplicate measurements of samples provided by the International Collaborative Study, and replicate measurements of the dilution of the 14C-labeled benzene standard. The variability in the measurements of the International Collaborative Study samples suggest the existence of systematic bias.

Description: It is clear that radiocarbon researchers take a forward view towards the improvement of accuracy and precision in dating. Unfortunately, archaeologists base much of their research on the published dates produced in the past. Archaeologists and other users of radiocarbon dates should understand the limitations associated with past dates. This article addresses these limitations by looking at a large number of routine radiocarbon dates associated with a block of English tree-ring chronologies, the true ages of which are now known within close limits. My conclusion supports the idea of global multiplication factors as proposed by the International Study Group (1982).

Description: The purpose of this Quality Assurance (QA) protocol is to summarize guidelines that have been accepted by directors of many radiocarbon dating laboratories throughout the world, and by the International Atomic Energy Agency (IAEA). Some laboratories have followed similar procedures successfully for years. Laboratories that carefully adhere to this protocol will produce consistently reliable data that will be comparable in accuracy to all other laboratories following this or any other equally rigorous quality assurance program. This statement does not, however, pertain to samples with 14C activities highly sensitive to method or degree of pretreatment, as pretreatment techniques vary among laboratories.

Description: A new high-pressure methane-filled counter system for 14C dating was installed in 1986 when the first stage of the International Collaborative Study (ICS) started. Random errors in the new measuring system and in the process of chemical pretreatment and preparation were checked during the three years of intercomparison. Results show that the most important source of error in our laboratory is gas contamination. This causes variation of the count rate to exceed the statistically expected variability. Other sources of error are also discussed and limits of their contributions are given.

Description: Results of the International Collaborative Study show an unexpectedly large scatter of individual dates as well as systematic biases. Very high values of linear correlation coefficients are observed for all results of Stage 2 and for benzene samples of Stage 1. We observed moderate correlations for carbonate samples and the lowest for natural samples of wood and peat of Stage 3. The correlation is practically negligible among results obtained in different stages. The probable reasons for such effects are seen in medium-term changes in the calibration of the counting systems.

Description: Radiocarbon activity of 11 modern marine shell samples from the New Zealand region is enhanced compared with the surface layers of the average world ocean. The measured enhancement, δR, is equivalent to −31 ± 13 years. On this basis, the Institute of Nuclear Sciences will now use a value of −30 years in reporting calibrated ages for marine shell samples.

Description: The 14C measurements reported here were made between 1983 and 1987. Sample pretreatment and date calculations were previously reported (Figini et al 1984). The method employed, liquid scintillation counting, was previously described (Huarte & Figini 1988). No 13C/12C ratios were measured and results were not corrected for 13C fractionation and/or reservoir effect. Descriptions, comments and references to publications are based on information supplied by submitters.

Description: Accelerator mass spectrometry dating of three 50g samples of marine turtle bone from the basal cultural stratum of the Tongoleleka archaeological site, Lifuka Island, Kingdom of Tonga, South Pacific yields results that agree with conventional 14C dates on marine shell. A method for calibrating these dates that takes into account the long distance migrations of marine turtles in the South Pacific is proposed. A sample size greater than 50g is recommended for routine AMS dating of marine turtle bone.

Description: We have studied the limitations of conventional mass spectrometry and have examined accelerator based methods which could help circumvent these limitations. In particular, cyclotron-based accelerator mass spectrometric (AMS) techniques are discussed with an emphasis on evaluating performances of superconducting mini-cyclotrons designed for use as AMS instruments. We discussed the design of superconducting mini-cyclotrons dedicated to radioisotope dating research.

Description: A theoretical approach towards predicting the carbon isotope composition of carbonate cave deposits is presented. The proposed model simulates time variations of both the chemical and isotopic composition of the carbonate solution and deposited calcite in the course of CaCO3 precipitation. Two phases of the precipitation process are distinguished and treated separately: initial outgassing of the solution until a certain degree of supersaturation of CO32- ions is reached and subsequent precipitation of CaCO3 related to further outgassing. Precipitation rates of CaCO3 predicted by the model agree fairly well with literature data. The model predicts δ13C values of deposited calcite within a range of ca −16 to +3‰ depending on temperature, chemical and isotope parameters of the initial solution and actual degree of the precipitation process.

Description: I describe here the establishment and use of statistical control graphs based on the analysis of variance for monitoring the stability of operation of radiocarbon dating counting systems.

Description: I describe here a series of routine self-checks that the Uppsala 14C laboratory performs with all measurements. We estimate all uncertainties in the physical measurement of a sample. We study long-term stability, calculate mean values for oxalic acid and background and compare expected and real statistical distributions of uncertainties. To reduce the risk of bias, the samples from each series are almost exclusively run on the same counter. Some samples are, however, run on two or more counters to check the possible bias to achieve reliable activity comparisons with other laboratories. It is always possible to trace which counter is used, since different number series are used for different counters.

Description: The Radiocarbon and Tritium Laboratory of the Rudjer Bošković Institute, Zagreb, participated in the International Collaborative Study (ICS) in all three stages. All measurements were made by proportional counting of methane. We present here a statistical analysis of our results. A comparison with the mean or median values of reported ICS values showed that our results are generally slightly younger.

Description: Following Harwell Measurements VI (Walker & Otlet 1988) this is the second of the series of lists of English archaeological dates commissioned for measurement by the Historic Buildings and Monuments Commission for England and Wales within prescribed contractual periods. This list, containing 176 dates, refers to the period, April 1986 to March 1987, and results are reported irrespective of whether the associated projects are completed or ongoing.

Description: An assessment is made of the credibility of the radiocarbon dating of the shroud of Turin. The quoted final results produced a calibrated calendar age range of AD 1260–1390 for the linen of the Turin shroud at a 95% confidence level. The measurements were carried out independently in three accelerator mass spectrometry (AMS) laboratories located at the University of Arizona, Tucson, Arizona, USA, Oxford University, Oxford, England, and ETH-Hönggerberg, Zürich, Switzerland with assistance for certification and data analysis provided by the British Museum. The author concludes that, although the procedures followed differed substantially from those recommended at a workshop organized by the Pontifical Academy of Sciences, the results are credible. Although of negligible scientific value, they represent a major public triumph for the AMS method of carbon dating. However, many doubts have been raised, both real and fanciful, concerning the validity of the results and these are discussed. It is suggested that steps should be taken to conserve the shroud and that permission should be given for its examination by experts in medieval art.

Description: We briefly present here the environmental isotope intercalibration programs of the International Atomic Energy Agency (IAEA). In fact, the IAEA has implemented two parallel programs during the last 20 years: for stable isotopes of light elements and for a radioactive isotope of hydrogen, tritium. This IAEA activity resulted in the preparation of a number of reference and intercomparison materials of various types, now stored in the Agency and available upon request.

Description: In closing this workshop, I must thank all of the delegates for making this meeting so very enjoyable for ourselves, the organisers. So much so that we will give serious thought to inviting you back to Scotland very soon. The meeting has, in our view, been eminently successful in the scientific sense. I believe that we have made uniquely important and fundamental observations and plans for the future of 14C dating. I would like to summarise quickly my personal view of the main findings of the workshop. I would start this by recalling the eight questions posed in my opening address. The questions and my impression of the workshop's answers are as follows:

Description: Most radiocarbon ages are readily accepted by researchers in all disciplines. It is recognized, however, that discrepancies appear in the literature. These problems have been highlighted by the International Collaborative Study. The introduction of quality control and assurance techniques used in some laboratories for many years could reduce or eliminate aberrant results. I present here some of the basic considerations of this approach in the processes of conventional radiocarbon dating.

Description: The results of this study indicate that scintillation counters employing burst-counting circuitry are capable of producing accurate age measurements. Replicate analyses confirm the validity of the minimum error of 50-60 years quoted on routine age measurements carried out at this laboratory.

Description: The results of the Glasgow Intercomparison Project and discussions about ways to increase a laboratory's quality as well as an archaeologist's confidence led to a general agreement at the Workshop about the outline of a procedure for Quality Control and Assurance. The scheme is primarily based on proposals presented by Dr Austin Long, University of Arizona, Dr Roberto Gonfiantini of the International Atomic Energy Agency and our Glasgow hosts. It consists of three elements:

Description: The use of computer data bases for storage and retrieval of 14C data is a logical application for the rapidly expanding numbers of 14C determinations. Harwell has established a data base for all samples originating from sites in the United Kingdom and Eire. The core of the data is the Council for British Archaeology's published Index of Radiocarbon Dates which we are expanding to include all Harwell UK dates released for publication by the submitters plus dates from other laboratories both within and outside the UK. As a demonstration of the feasibility of direct database-to-database communication, cooperation has been sought from Groningen and Oxford to transfer computer files containing 14C results for UK sites. Neither of these laboratories use the same system as Harwell for their in-house data base and this exercise highlights the importance of a transfer language for both the national and international schemes as it is no longer practical to carry out such procedures through keyboard typing.

Description: I conducted a high-precision comparison at the 0.2% to 0.3% level with samples supplied by the radiocarbon laboratory of the Quaternary Research Center at the University of Washington (QRC). Four samples with ages ranging from modern to 〉 50,000 BP were dated in a blind test. The absence of cosmic-radiation background in AMS dating is a major advantage for dating samples 〉 35,000 BP. The reliability of AMS dates 〉 35,000 BP depends entirely on understanding the contamination processes. By comparing results with laboratories capable of sample enrichment, such as QRC, it is possible to identify and estimate the intrinsic 14C in the background samples as well as the contamination introduced by sample preparation.

Description: The current intercomparison of data from 14C laboratories reveals significant variability among liquid scintillation laboratories, suggesting that identical samples submitted to different laboratories may yield values that differ by much more than expected on a purely statistical basis. Erroneous dates (recently corrected) by a well-established 14C laboratory give rise to further concern for quality 14C data. Thus, it is incumbent on each laboratory to develop and implement a quality assurance and control (QA/QC) program in order to ensure accuracy of results and to alert lab personnel to problems.

Description: Many interlaboratory studies have been made in the 14C community at irregular intervals over the past ten years. At times, the results from these studies have been contentious, mostly because of the lack of consistency in their findings. The importance of regular exercises has become particularly acute due to the large number of operating laboratories and the diversity of their methodologies. Hence, we briefly review the studies that have been made in the 1980s, focusing on those in which our laboratories participated. These include the 14C Interlaboratory Comparison in the UK (Otlet et al 1980), the International Comparison (ISG 1982, 1983) and the first two parts of the current International Collaborative Program (Scott et al 1989a, b). The development of each study, its findings and shortcomings, are highlighted in order to assess the concordance of the conclusions.

Description: The purpose of this Quality Assurance (QA) protocol is to summarize guidelines that have been accepted by the majority of directors of radiocarbon dating laboratories throughout the world, and by the International Atomic Energy Agency (IAEA). Laboratories that carefully adhere to this protocol will produce consistently reliable data which will be comparable in accuracy to all other laboratories following this or any other equally rigorous quality assurance program. This statement does not, however, pertain to samples with 14C activities highly sensitive to method or degree of pretreatment, as pretreatment techniques vary among laboratories.

Description: Procedures and equipment used in the University of Wisconsin laboratory have been described in previous date lists (Bender, Bryson & Baerreis 1965; Steventon & Kutzbach 1986). Except as otherwise indicated, wood, charcoal and peat samples are pretreated with dilute NaOH-NA4P2O7 and dilute H3PO4 before conversion to counting gas methane; when noted, marls and lake cores are treated with acid only. Very calcareous materials are treated with HCL instead of H3PO4.

Description: 14C dates of relict tufa deposits at Gordale indicated a Subboreal age when the carbonate age was corrected with empirical bedrock dilution factors ‘q’ of 0.79 or 0.85. Estimates of ‘apparent age,’ based on extrapolated δ13C values were about twice those obtained with q, and the 1σ error was large. The δ13C values of tufa samples were not correlated with carbonate age and were close to −10. Application of q values in this district requires caution as they appear to be site-specific. We recommend that wherever possible, levels of 13C and 14C are measured in the associated tufa-depositing water, and an empirical dilution factor employed.

Description: An extensive experimental investigation of the binary collision dynamics of water drops for size ratios of 1, 0.75, and 0.5, for the Weber-number range of 1 to 100, and for all impact parameters is reported. Two different types of separating collisions, namely reflexive and stretching separations, are identified. Reflexive separation is found to occur for near head-on collisions, while stretching separation occurs for large-impact-parameter collisions. The boundaries between both of the separatingcollisions and coalescence collision are found experimentally. Theoretical models for predictions of the reflexive and stretching separation are also given. © 1990, Cambridge University Press. All rights reserved.

Description: This paper describes supersonic flows of a gas—particle mixture around a sphere. The Euler equations for a gas-phase interacting with a particle one are solved by using a TVD (Total Variation Diminishing) scheme developed by Chakravarthy & Osher, and the particle phase is solved by applying a discrete particle-cloud model. First, steady two-phase flows with a finite loading ratio are simulated. By comparing in detail the dusty results with the dust-free ones, the effects of the presence of particles on the flow field in the shock layer are clarified. Also an attempt to correlate the particle behaviours is made with universal parameters such as the Stokes number and the particle loading ratio. Next, non-steady two-phase flows are treated. Impingement of a large particle-cloud on a shock layer of a dust-free gas in front of a sphere is numerically simulated. The effect of particles rebounded from the sphere is taken into account. It is shown that a temporal reverse flow region of the gas is induced near the body axis in the shock layer, which is responsible for the appearance of the gas flow region where the pressure gradient becomes negative along the body surface. These phenomena are consistent with the previous experimental observations. It will be shown that the present results support a flow model for the particle-induced flow field postulated in connection with ‘heating augmentation’ found in the heat transfer measurement in hypersonic particle erosion environments. The particle behaviour in such flows is so complicated that it is almost impossible to treat the particle phase as an ordinary continuum medium. © 1990, Cambridge University Press. All rights reserved.

Description: An experimental investigation of the sedimentation of monodisperse colloidal silica spheres with grafted octadecyl chains with three different interaction potentials is presented. Small particles (0.27 µm) behaved as hard spheres in cyclohexane, but larger ones (0.60 and 0.94 µm) are weakly flocculated by van der Waals attractions. The smallest particles (0.08 µm) in hexadecane are strongly flocculated by attractions between the octadecyl layers. A medical computer tomography (CT) scanner provided an accurate and absolute density measurement without disrupting the process. For the hard spheres and the weakly flocculated systems, the kinetics of sedimentation for the dispersed phase could readily be predicted utilizing the flux curve. For flocculated networks, we found a power–law relationship between compressive yield stresses and solids fractions comparable with other experimental systems. © 1990, Cambridge University Press. All rights reserved.

Description: An experimental study of surface waves parametrically excited by vertical vibrations is presented. The shape of the eigenmodes in a closed vessel, and the importance of the free-surface boundary conditions, are discussed. Stability boundaries, wave amplitude, and perturbation characteristic time of decay are measured and found to be in agreement with an amplitude equation derived by symmetry. The measurement of the amplitude equation coefficients explains why the observed transition is always supercritical, and shows the effect of the edge constraint on the dissipation and eigen frequency of the various modes. The fluid surface tension is obtained from the dispersion relation measurement. Several visualization methods in large-aspect-ratio cells are presented.

Description: Cocke (1969) showed that, on average, infinitesimal material lines and surfaces are stretched in incompressible isotropic turbulence. We have extended those results to obtain upper and lower bounds for the stretching of such infinitesimal elements in terms of the eigenvalues of the Green deformation tensor. These bounds are in turn used to find bounds for the stretching of finite material lines and surfaces. © 1990, Cambridge University Press. All rights reserved.

Description: The problem is solved of the flow due to a rapidly oscillating source situated near a plane surface with a hemispherical indentation. The strength of the far-field flow is evaluated, and also the natural frequency of oscillation of a small bubble centred at the same position as the source. © 1990, Cambridge University Press. All rights reserved.

Description: The characteristics of near-wall turbulence are examined and the result is used to assess the behaviour of the various terms in the Reynolds-stress transport equations. It is found that all components of the velocity-pressure-gradient correlation vanish at the wall. Conventional splitting of this second-order tensor into a pressure diffusion part and a pressure redistribution part and subsequent neglect of the pressure diffusion term in the modelled Reynolds-stress equations leads to finite near-wall values for two components of the redistribution tensor. This, therefore, suggests that, in near-wall turbulent flow modelling, the velocity–pressure–gradient correlation rather than pressure redistribution should be modelled. Based on this understanding, a methodology to derive an asymptotically correct model for the velocity–pressure–gradient correlation is proposed. A model that has the property of approaching the high–Reynolds–number model for pressure redistribution far away from the wall is derived. A similar analysis is carried out on the viscous dissipation term and asymptotically correct near-wall modifications are proposed. The near–wall closure based on the Reynolds–stress equations and a conventional low–Reynolds–number dissipation–rate equation is used to calculate fully–developed turbulent channel and pipe flows at different Reynolds numbers. A careful parametric study of the model constants introduced by the near–wall closure reveals that one constant in the dissipation–rate equation is Reynolds–number dependent, and a preliminary expression is proposed for this constant. With this modification, excellent agreement with near–wall turbulence statistics, measured and simulated, is obtained, especially the anisotropic behaviour of the normal stresses. On the other hand, it is found that the dissipation–rate equation has a significant effect on the calculated Reynolds–stress budgets. Possible improvements could be obtained by using available direct simulation data to help formulate a more realistic dissipation–rate equation. When such an equation is available, the present approach can again be used to derive a near–wall closure for the Reynolds–stress equations. The resultant closure could give improved predictions of the turbulence statistics and the Reynolds–stress budgets. © 1990, Cambridge University Press. All rights reserved.

Description: We study the relationship between dynamical structure and shape for vortex pairs, now usually named ‘modons’. When the boundary between the exterior irrotational flow and the inner core of non-zero vorticity is a circle, an analytical solution is known. Here, we generalize the circular modons to solitary vortex pairs whose vorticity boundary is an ellipse. We find that as the eccentricity of the ellipse increases, the vorticity becomes concentrated in narrow ridges which run just inside the elliptical vorticity boundary and continue just inside the line of zero vorticity which divides the two vortices. Each vortex becomes increasingly ‘hollow’ in the sense that each contains a broad valley of low vorticity which is completely enclosed by the ridge of high vorticity already described. The relationship between vorticity ζ and streak function Ψ, which is linear for the circular modons, becomes strongly nonlinear for highly eccentric modons, qualitatively resembling ζ ∝ Ψe−λΨ for some constant λ. In this study, we neglect the Earth's rotation, but our method is directly applicable to quasi-geostrophic modons, too. An efficient and simple spectral method for modon problems is provided.

Description: An X-ray attenuation technique is used to obtain the local concentration of spherical particles in a polydisperse suspension as a function of vertical position and time. From these experimental data, the average velocity of sedimentation in the homogeneous part of the suspension is derived by considering the variation with time of the total volume of particles located above a given fixed horizontal plane. Measurements have been performed in suspensions of particles which differ from each other in size with a total volume concentration in particles between 0.13% and 2.5%, and also in suspensions of particles which differ from each other both in size and in density, the total volume concentration being 2%. For the first kind of suspension, the experimental hindered settling factor is plotted versus the concentration and a linear regression analysis provides the slope with its 90% confidence limits: Se = −5.3 ± 1.1. This experimental average coefficient of sedimentation is in good agreement with the theoretical average coefficient St = −5.60 obtained from the results of Batchelor & Wen (1982). The second kind of suspension, for which permanent doublets of spheres may theoretically exist, is not in the range of validity of Batchelor & Wen's results. The experimental average coefficient of sedimentation for this case is found to be much larger than the prediction obtained by extrapolating Batchelor & Wen's results out of their range of validity. This increased velocity may be experimental evidence of the existence of permanent doublets.

Description: The physical mechanisms for vortex breakdown which, it is proposed here, rely on the production of a negative azimuthal component of vorticity, are elucidated with the aid of a simple, steady, inviscid, axisymmetric equation of motion. Most studies of vortex breakdown use as a starting point an equation for the azimuthal vorticity (Squire 1960), but a departure in the present study is that it is explored directly and not through perturbations of an initial stream function. The inviscid equation of motion that is derived leads to a criterion for vortex breakdown based on the generation of negative azimuthal vorticity on some stream surfaces. In viscid predictions are tested against results from numerical calculations of the Navier—Stokes equations for which breakdown occurs. © 1990, Cambridge University Press. All rights reserved.

Description: We have investigated the effect of a solidifying crust on the dynamics and surface morphology of radial viscous-gravity currents. Liquid polyethylene glycol was admitted into the base of a tank filled with cold sucrose solution maintained at a temperature below the wax freezing point. As the radial current advanced away from the inlet, its surface solidified and deformed through a combination of folding and fracturing. For the warmest experiments, during which solidification did not occur, the radius of the current increased in proportion to the square root of time, as demonstrated both experimentally and theoretically for isothermal viscous fluids by Huppert (1982). When cooling was sufficiently rapid, solid crust formed and caused the spreading rate to decrease. A cooling model combining conduction in the wax with convection in the sucrose solution predicts the distance from the source at which the solid crust first appeared. Progressively colder experiments revealed a sequence of surface morphologies which resembled features observed on cooling lava flows and lava lakes. Flows in which crust formed very slowly developed marginal levees which contained and channelled the main portion of the current. Colder flows with more rapid crust growth formed regularly spaced surface folds, multi-armed rift structures complete with shear offsets, and bulbous lobate forms similar to pillow lavas seen under the ocean. The same transitions between modes of surface deformation were also generated by keeping the ambient water temperature constant and decreasing the extrusion rate. This demonstration that surfaces can exhibit a well-defined sequence of morphologies which depend on the underlying flow conditions offers the prospect of more successful interpretation of natural lava flows. © 1990, Cambridge University Press. All rights reserved.

Description: The problem of buoyancy-induced Stokes flow in a sectorial region is addressed. Skew-symmetric flows are considered for wedge or opening angles of the sector in the range 0 〈 α ≤ π. The basic structure and character of the motion are found to depend critically upon the relative dominance, near the sector vertex, of the particular solution of the system with respect to the leading eigenfunction. A simple criterion is developed for the appearance of eddies, such as those observed by Moffatt (1964), in the neighbourhood of the sector vertex. A calculation is carried out for the specific case of motion induced by different temperatures on the radial boundaries of the enclosure. It is found that corner eddies may be present in this circumstance for wedge angles in the range 126º ≲ α ≲146º. The eddying motion near the vertex is examined, in some detail, for the wedge angle α = 135º. In the limiting case of α = π, corresponding to a semicircular-shaped sector, the particular solution is found to exhibit singular behaviour. However, this singular nature is found to be spurious, as a bounded particular solution can be constructed with the aid of one of the eigensolutions. Results are given for no-slip and shear-free conditions on the circular boundary of the sector for the purpose of comparison. © 1990, Cambridge University Press. All rights reserved.

Description: Local baroclinic instability is studied in a two-layer quasi-geostrophic model. Variable meridional bottom slope controls the local supercriticality of a uniform zonal flow. Solutions are found by matching pressure, velocity, and upper-layer vorticity across longitudes where the bottom slope changes abruptly so as to destabilize the flow in a central interval of limited zonal extent. In contrast to previous results from heuristic models, an infinite number of modes exist for arbitrarily short intervals. For long intervals, modal growth rates and frequencies approach the numerical and WKB results for the most unstable mode. For intervals of length comparable to and smaller than the wavelengths of unstable waves in the homogeneous problem, the WKB results lose accuracy. The modes retain large growth rates (about half maximum) for intervals as short as the internal deformation radius. Evidently, the deformation radius and not the homogeneous instability determines the fundamental scale for local instability. Maximum amplitudes occur near the downstream edge of the unstable interval. Lower-layer amplitudes decay downstream more rapidly than upper-layer amplitudes. For short intervals, the instability couples motions with widely disparate horizontal scales in the upper and lower layers. Heat flux is more strictly confined than amplitude. Growth rates increase linearly with weak supercriticality. © 1990, Cambridge University Press. All rights reserved.

Description: The flow past a cylindrical obstacle in an enclosed channel is examined when the entire configuration is rotating rapidly about an axis which is aligned with that of the obstacle. When viewed from a frame of reference which is rotating with the channel, Coriolis forces dominate and act to constrain the motion to be two-dimensional. The channel is considered to have depth varying linearly across its width, producing effects equivalent to the so-called β-plane approximation and permitting waves to travel away from the obstacle, both upstream and downstream. For the eastward flow considered in this paper, this leads to the formation of a lee-wavetrain downstream of the obstacle and, under some conditions, a region of retarded, or ‘blocked’, flow upstream of the obstacle. The flow regime studied is essentially inviscid, although one form of frictional effect on the flow, introduced through the Ekman layers, isincluded. The properties of this system are examined numerically and compared with the theoretical predictions from other studies, which are applicable in asymptotic limits of the parameters. In particular, the relevance of ‘Long's model’ solutions is considered. © 1990, Cambridge University Press. All rights reserved.

Description: Non–parallel effects which are due to the growing boundary layer are investigated by direct numerical integration of the complete Navier—Stokes equations for incompressible flows. The problem formulationis spatial, i.e. disturbances may grow or decay in the downstream direction as in the physical experiments. In the past various non-parallel theories were published that differ considerably from each other in both approach and interpretation of the results. In this paper a detailed comparison of the Navier—Stokes calculation with the various non-parallel theories is provided. It is shown, that the good agreement of some of the theories with experiments is fortuitous and that the difference between experiments and theories concerning the branch I neutral location cannot be explained by non-parallel effects. © 1990, Cambridge University Press. All rights reserved.

Description: The Navier—Stokes equations for flow in a rotating circular pipe are solved numerically, subject to imposing helical symmetry on the velocity field ν = ν(γ, θ+αz, t). The helical symmetry is exploited by writing the equations of motion in helical variables, reducing the problem to two dimensions. A limited study of the pipe flow is made in the parameter space of the wavenumber α, and the axial and azimuthal Reynolds numbers. The steadily rotating waves previously studied by Toplosky & Akylas (1988), which arise from the linear instability of the basic steady flow, are found to undergo a series of bifurcations, through periodic to aperiodic time dependence. The relevance of these results to the mechanism of laminar—turbulent transition in a stationary pipe is discussed. © 1990, Cambridge University Press. All rights reserved.

Description: The extended Korteweg-de Vries equation which includes nonlinear and dispersive terms cubic in the wave amplitude is derived from the water-wave equations and the Lagrangian for the water-wave equations. For the special case in which only the higher-order nonlinear term is retained, the extended Korteweg-de Vries equation is transformed into the Korteweg-de Vries equation. Modulation equations for this equation are then derived from the modulation equations for the Korteweg-de Vries equation and the undular bore solution of the extended Korteweg-de Vries equation is found as a simple wave solution of these modulation equations. The modulation equations are also used to extend the solution for the resonant flow of a fluid over topography. This resonant flow occurs when, in the weakly nonlinear, long-wave limit, the basic flow speed is close to a linear long-wave phase speed for one of the long-wave modes. In addition to the effect of higher-order terms, the effect of boundary-layer viscosity is also considered. These solutions (with and without viscosity) are compared with recent experimental and numerical results.

Description: In this paper, selected findings of a detailed experimental investigation are reported concerning the effects of forced free-stream unsteadiness on a turbulent boundary layer. The forced unsteadiness was sinusoidal and was superimposed locally on an otherwise-steady mainstream, beyond a turbulent boundary layer which had developed under constant-pressure conditions. Within the region over which freestream unsteadiness was induced, the sinusoidal variation in pressure gradient was between extremes of zero and a positive value, with a positive average level. The local response of the boundary layer to these free-stream effects was studied through simultaneous measurements of the u– and v-components of the velocity field. Although extensive studies of unsteady, turbulent, fully-developed pipe and channel flow have been carried out, the problem of a developing turbulent boundary layer and its response to forced free-stream unsteadiness has received comparatively little attention. The present study is intended to redress this imbalance and, when contrasted with other studies of unsteady turbulent boundary layers, is unique in that: (i) it features an appreciable amplitude of mainstream modulation a t a large number of frequencies of forced unsteadiness, (ii) its measurements are both detailed and of high spatial resolution, so that the near-wall behaviour of the flow can be discerned, and (iii) it allows local modulation of the mainstream beyond a turbulent boundary layer which has developed under the well-known conditions of steady, twodimensional, constant-pressure flow. Results are reported which allow comparison of the behaviour of boundary layers under the same mean external conditions, but with different time dependence in their free-stream velocities. These time dependences correspond to: (i) steady flow, (ii) quasi-steadily varying flow, and (iii) unsteady flow a t different frequencies of mainstream unsteadiness. Experimental results focus upon the time-averaged nature of the flow; they indicate that the mean structure of the turbulent boundary layer is sufficiently robust that the imposition of free-stream unsteadiness results only in minor differences relative to the mean character of the steady flow, even at frequencies for which the momentary condition of the flow departs substantially from its quasi-steady state. Mean levels of turbulence production are likewise unaffected by free-stream unsteadiness and temporal production of turbulence appears to result only from modulation of the motions which contribute to turbulence production as a time-averaged measure. © 1990, Cambridge University Press. All rights reserved.

Description: Natural convection in a Boussinesq fluid filling the narrow gap between two isothermal, concentric spheres at different temperatures depends strongly on radius ratio, Prandtl number, and Grashof number. When the inner sphere has a higher temperature than the outer sphere, and for fixed values of radius ratio and Prandtl number, experiments show the flow to be steady and axisymmetric for sufficiently small Grashof number and quasi-periodic and axisymmetric for Grashof numbers greater than a critical value. It is our hypothesis that the observed transition is a flow bifurcation. This hypothesis is examined by solving an appropriate eigenvalue problem. The critical Grashof number, critical eigenvalues, and corresponding eigenvectors are obtained as functions of the radius ratio, Prandtl number, and longitudinal wavenumber. Critical Grashof numbers range from 1.18* 104 to 2.63 * 103 as Prandtl number Pγ increases from zero to 0.7, for radius ratios of 0.900 and 0.950. A transitional Prandtl number Prt exists such that for Pγ 〈 Prt the bifurcation is time-periodic and axisymmetric. For Pγ 〉 Pγtthe bifurcation is steady and non-axisymmetric with wavenumber two. A first approximation to the bifurcated flow is obtained using the critical eigenvectors. For Pγ 〈 Pγtthe bifurcation sets in as a cluster of relatively strong cells with alternating directions of rotation. The cells remain fixed in location, but pulsate with time. The cluster moves toward the top of the annulus as Pγ increases toward Prt. An important feature of the non-axisymmetric bifurcation for Pγ 〉 Prt is a set of four cells located at each pole of the annulus in which the radial velocity alternates direction in moving from any one cell to an adjacent one. For fixed radius ratio, the average Nusselt number at criticality varies only slightly with Prandtl number. © 1990, Cambridge University Press. All rights reserved.

Description: Thermoeapillary convection arising in small-depth layers (long horizontal cavities) subject to a horizontal temperature gradient is studied numerically. A broad range of values of the Reynolds-Marangoni number, Re, is considered for three values of the aspect ratio (A = length/height). For the largest aspect ratio considered, A = 25, the fully developed Poiseuille—Couette solution is reached, but only for moderate Re. The limiting Re value for the observability of such a fully developed solution is derived as a function of A(Re ≤ 20A). For Re ≤ 20A, the flow exhibits three distinct regimes, in the upwind, central and downwind regions, respectively. The Poiseuille—Couette solution (when it exists) fills the central region, and the flow is accelerated, in the upwind region, to reach this Poiseuille—Couette solution at a distance that is proportional to Re. In the downwind region, where the flow is deflected by the endwall, a multi-roll structure is exhibited for Re ≥ 1330. The number of rolls increases with Re. When Re 〈 20A, the upwind and downwind regions coalesce and some of the downwind rolls can be suppressed. Most of the computations concern interfacial conditions (with fixed temperature distribution) for which the dynamical solution is decoupled from the thermal one. A few thermal solutions are given herein, for Pr = 0.015 only. © 1990, Cambridge University Press. All rights reserved.

Description: The evolution of a turbulent spot in an accelerating laminar boundary-layer flow was investigated. The type of boundary layer chosen for this experiment resembles in every respect the flow in the vicinity of a stagnation point theoretically described by Falkner and Skan. The rate of growth of the spot was significantly inhibited by the favourable pressure gradient in all three directions. It became much shorter and narrower in comparison with a similar spot generated in a Blasius boundary layer at comparable distances from its origin and comparable Reynolds numbers. The celerities of its boundaries did not scale with the local free-stream velocity as they do in the absence of a pressure gradient. Dimensional analysis was used to identify and correlate the independent variables determining the size, the convection speed, and the relative rate of growth of this spot. The familiar arrowhead shape of the spot gave way to a rounded triangular shape with the trailing interface being straight and perpendicular to the direction of streaming. The familiar Tollmien-Schlichting wave packet was not observed in this pressure gradient because the surrounding boundary layer was very stable at the Reconsidered. Since the arrowhead shape of the spot is associated with the breakdown of the waves within the packet it cannot occur below the critical Re. The relative size of the calmed region following the spot also diminished however, one could only speculate as to the origin of this region. © 1990, Cambridge University Press. All rights reserved.

Description: Small–amplitude wave motion in an inert gas confined between a moving piston and a fixed cylinder endwall is studied using the unsteady Euler equations. The waves, generated by either initial disturbances or piston motion, reflect back and forth in the cylinder on the acoustic timescale. The accumulated effect of these waves controls the bulk variations of velocity and thermodynamic variables on the longer piston timescale. Perturbation methods, based on the small ratio of acoustic to piston time, are employed to formulate the gasdynamic problem. The application of multiple timescaling allows the gasdynamic wave field to be separated from the bulk response of the gas. The evolution of the wave phenomena, including nonlinear wave deformation and weak shock formation during the piston passage time, is described in terms of time–dependent Fourier series solutions, whose coefficients are computed from a truncated system of coupled nonlinear ordinary differential equations. The long–time asymptotic flow field after shock formation is sawtooth–like, in which case the Fourier modes become decoupled. A remarkably simple relation between the shock amplitude and piston velocity is discovered. It is demonstrated that (i) the wave amplitude and frequency strongly depend on the piston motion; (ii) shock waves can be damped in a significant way by internal dissipation; and (iii) the mathematical approach developed in this study possesses certain advantages over the more traditional method of characteristics. © 1990, Cambridge University Press. All rights reserved.

Description: We examine weak second-sound waves in He II at temperatures and pressures near one of the zeros of the Khalatnikov steepening parameter Γ. An extension of the reductive perturbation scheme of Taniuti & Wei is employed to derive the cubic Burgers’ equation governing these waves. It is shown that mixed nonlinearity may occur in disturbances in which the local value of Γ remains strictly positive or strictly negative. Further new results include expressions for the shock speed, shock structure and the conditions under which the shock thickness increases, rather than decreases, with strength. The fundamental existence conditions for temperature shocks are also delineated and related to the shock disintegration process observed in experimental studies. © 1990, Cambridge University Press. All rights reserved.

Description: An angular spectrum model for predicting the transformation of Stokes waves on a mildly varying topography is developed, including refraction, diffraction, shoaling and nonlinear wave interactions. The equations governing the water-wave motion are perturbed using the method of multiple scales and Stokes expansions for the velocity potential and free-surface displacement. The first-order solution is expressed as an angular spectrum, or directional modes, of the wave field propagating on a beach with straight iso-baths whose depth is given by laterally averaged depths. The equations for the evolution of the angular spectrum due to the effectsof bottom variation and cubic resonant interaction are obtained from the higher-order problems. Comparison of the present model with existing models is made for some simple cases. Numerical examples of the time-independent version of the model are presented for laboratory experiments for wave diffraction behind a breakwater gap and wave focusing over submerged shoals: An elliptic shoal on a sloping beach and a circular shoal on a flat bottom. © 1990, Cambridge University Press. All rights reserved.

Description: The paper is concerned with the problem of the linear stability of an arbitrary inviscid zonal flow on a β-plane. Based on the analysis of integral relations following from the linear boundary-value problem, new evaluations, considerably more exact than the previously known ones, of the parameter region of unstable disturbances are derived. Some new relations among these bounds are established. © 1990, Cambridge University Press. All rights reserved.

Description: Turbulence in solid-body rotation is generated by a flow of air passing through a rotating cylinder containing a dense honeycomb structure and a turbulence-producing grid. The velocity field is probed downstream of this device by hot-wire probes. Using the statistical quantities characterizing the fluctuating field, we show that the rotation affects mainly the components normal to the rotation axis and that these effects are triggered when the Rossby numbers constructed from macroscopic turbulent quantities, are less than unity. These results are discussed in the framework of other available experimental results on the subject. A theoretical interpretation, chiefly based on spectral analysis, is then proposed to explain the trends of the observations.

Description: The problem of viscous fingering in a Hele-Shaw cell with moving contact lines is considered. In contrast to the usual situation where the displaced fluid coats the solid surface in the form of thin films, here, both the displacing and the displaced fluids make direct contact with the solid. The principal differences between these two situations are in the ranges of attainable values of the gapwise component of the interfacial curvature (the component due to the bending of the fluid interface across the small gap of the Hele-Shaw cell), and in the introduction of two additional parameters for the case with moving contact lines. These parameters are the receding contact angle, and the sensivity of the dynamic angle to the speed of the contact line. Our objective is the prediction of the shape and widths of the fingers in the limit of small capillary number, Uμ/σ. Here, U denotes the finger speed, μ denotes the dynamic viscosity of the more viscous displaced fluid, and σ denotes the surface tension of the fluid interface. As might be expected, there are similarities and differences between the two problems. Despite the fact that different equations arise, we find that they can be analysed using the techniques introduced by McLean & Saffman and Vanden-Broeck for the thin-film case. The nature of the multiplicity of solutions also appears to be similar for the two problems. Our results indicate that when contact lines are present, the finger shapes are sensitive to the value of the contact angle only in the vicinity of its nose, reminiscent of experiments where bubbles or wires are placed at the nose of viscous fingers when thin films are present. On the other hand, in the present problem at least two distinct velocity scales emerge with well-defined asymptotic limits, each of these two cases being distinguished by the relative importance played by the two components of the curvature of the fluid interface. It is found that the widths of fingers can be significantly smaller than half the width of the cell.

Description: The different modifications of the models of two-phase multicomponent filtration (Collins 1961; Nikolaevsky et al. 1968) enable one to study the dynamics of filtration flows, taking into account phase transitions. The equations of multicomponent filtration are quite complicated and only in a few individual cases do they allow for an exact solution. The most frequently used of these appears to be the solution of the stationary problem of the flow of a multicomponent mixture toward a well or a system of wells (Khristianovich 1941). In the present paper we show that at certain values of pressure, temperature and composition of the multicomponent mixture a stationary solution of the problem may not exist. The absence of a stationary solution is related to the possibility of a spatially homogeneous solution losing its stability under a perturbation (Mitlin 1986a, 1987b). We obtain an analytical criterion for instability. As an illustration, we present the results of the numerical solution of the planar linear problem of the evolution of a multicomponent system whose pressure and composition are perturbed with respect to their constant values, which are equal at both ends. We have done a numerical analysis of the plane-radial problem of the operation of a gas–condensate well with different mass fluxes, applying the conditions of a real deposit. There are several ranges of flux where the flow becomes pulsating. It is shown that the time within which the stationary solution sets in is a non-monotonic function of flux and on approaching the stability limit diverges in inverse proportion to the undercriticality of debit. We have analysed the connection between the observed instabilities and the thermodynamics of two-phase multicomponent mixtures. It is shown that the instabilities are associated with the system entering the region of retrograde condensation. We discuss the relation of retrograde phenomena to the effect of negative volume of heavy components and, as a consequence, to the negative compressibility of an individual volume of a two-phase mixture moving in a porous medium. It is shown that the observed autowave modes are relaxation oscillations in a distributed system. By using the method of perturbations in the interphase equilibrium time, we have analysed the loss of stability in a more general – non-equilibrium – model. We show that the instabilities are generated according to the Landau–Hopf scenario and calculate the period of auto-oscillations. The one-mode approximation of the theory leads to the Van der Pol equation. In conclusion we present an experimental confirmation of the theory.

Description: The paper is a continuation of work published in Boubnov & Golitsyn (1986). We present new measurements of the temperature and velocity field patterns and their statistical characteristics. This allows us to classify regimes of convection in a plane rotating horizontal fluid layer in terms of Rayleigh and Taylor numbers. Within the irregular regimes geostrophic convection is found for which the Rossby number is much less than unity. In the regular regimes the mean temperature profiles are linear with height in the bulk of the fluid, the gradient being dependent mainly on rotation rate Ω and fluid depth h. These together with some dimensional arguments lead to the heat transfer relationship Nu oc Raz Ta 2 between Nusselt, Rayleigh and Taylor numbers. Experimental results by Rossby (1969) and theoretical work by Chan (1974) and Riahi (1977) suggested this dependence. The dependence on ωΤ of the temperature power spectrum normalized by the variance was found to be universal at higher frequencies for all irregular convective motions, where Τ is the timescale of the thermal boundary layer for cases with a small influence of rotation and with Τ about three times larger (in numerical coefficient) for geostrophic convection. For irregular geostrophic regimes it is found that the temperature variance depends on rotation rate and heat flux, and is inversely proportional to the buoyancy parameter. Horizontal and vertical components of the velocity fields were measured for regular as well as irregular regimes, confirming, especially for geostrophic convection, the theoretical results by Golitsyn (1980). In conclusion some geophysical applications are briefly mentioned. © 1990, Cambridge University Press. All rights reserved.

Description: Motivated by problems concerning the storage and subsequent escape of the solar magnetic field we have studied how a magnetic layer embedded in a convectively stable atmosphere evolves due to axisymmetric instabilities driven by magnetic buoyancy. The initial equilibrium consists of a toroidal field sheared by a weaker poloidal component. The linear stability problem is investigated for both ideal and resistive MHD, and the nonlinear evolution is followed by numerical integration of the equations of motion. In all cases we found that the instability is greatly affected by the distribution and strength of the poloidal field. In particular, both the horizontal and vertical scales of the motions are controlled by the location of the surface on which the poloidal field vanishes - the resonant surface. In the nonlinear regime, a resonant surface close to the interface between the magnetized and field-free fluid leads to the localization of the instability so that only a fraction of the magnetic region is disrupted by the motions. By contrast, a deeply seated resonant surface leads to the complete disruption of the layer and to the formation of large, helical magnetic fragments whose identity is preserved for the entire simulation. © 1990, Cambridge University Press. All rights reserved.

Description: Solutions are obtained for hypersonic viscous interaction along a flat plate in the presence of strong boundary-layer blowing, with inverse-square-root injection velocity, for laminar flow over a cold wall and with a power-law viscosity-temperature relation. In the strong-interaction region, self-similarity is preserved if the blowing is such that the thicknesses of the inviscid shock layer, viscous shear layer, and inviscid blown layer all have the same order of magnitude. The weak-interaction region is also considered, and an approximate interpolation is used to join the solutions for the surface pressure. Certain difficulties in asymptotic matching are discussed, and the extension to flow past a thin wedge is shown. © 1990, Cambridge University Press. All rights reserved.

Description: The surface-tension-driven breakup of viscous jets is observed for a range of Weber and Ohnesorge numbers. The breakup is enhanced with a sinusoidal modulation or pulsation of the jet's exit velocity; the velocity modulation amplitudes and wavenumbers are larger than previous values reported in the literature. The combinations of modulation amplitude and wavenumber that produce uniform droplets are identified for each pair of Weber and Ohnesorge numbers. Satellite droplets are eliminated at values of the Ohnesorge number greater than 1.6. Droplet pairing and merging occurs at high wavenumbers droplet merging has not been reported in the jet breakup literature. The timescale for breakup is predicted within the data scatter by the thin filament equation of Bousfield et al. (1986) with no fitted parameters. An upper bound on satellite droplet size is predicted by the thin-filament equation and the average satellite droplet volume is qualitatively predicted. An algebraic expression is derived to predict the breakup time of viscous jets with large velocity modulation amplitudes. © 1990, Cambridge University Press. All rights reserved.

Description: The nature of the non-equilibrium flow of strongly dissociating nitrogen has been investigated by a series of simulation calculations using non-equilibrium (finite rate) chemical reactions. These were made with the equilibrium flux method (EFM), and the results have been found to compare favourably with experimental results obtained with a free-piston driven shock-tube wind tunnel which was used to obtain interferograms of the flow of pure nitrogen over a blunt-nosed body, 65 mm long at three angles of incidence. No simple relation between the flow with non-equilibrium chemistry and those for frozen or equilibrium chemistry has been found. The problems of relating test flows produced in the shock tunnel to flight conditions are investigated by considering the test flows that might be produced by some ‘ideal equivalent wind tunnels ‘. It is shown that the degree of frozen dissociation in the test flow in a shock tunnel is not a serious matter, but that the large difference in Mach number between shock tunnel flows and flight conditions may be more important. © 1990, Cambridge University Press. All rights reserved.

Description: The nonlinear Rayleigh–Taylor instability of a liquid layer resting on a plane wall below a second liquid of higher density is considered. Under the assumption of creeping flow, the motion is studied as a function of surface tension and the ratio of the viscosities of the two fluids. The flow induced by the deformation of the layer is represented by an interfacial distribution of Green's functions. A Fredholm integral equation of the second kind is derived for the density of the distribution, and is solved by successive iteration. The results show that for small and moderate surface tension, the instability of the layer leads to the formation of a periodic array of viscous plumes which penetrate into the overlying fluid. The morphology of these plumes strongly depends upon the viscosity ratio and surface tension. When the viscosity of the overlying fluid is comparable with or larger than that of the layer, the plumes are composed of a well-defined leading drop on top of a narrow stem. When the viscosity of the overlying fluid is smaller than that of the layer, the plumes take the form of a compact column of rising fluid. The size of the drop leading a plume is roughly proportional to the initial thickness of the layer. When surface tension is sufficiently small, ambient fluid is entrained into the leading drop and circulates in a spiral pattern. Convection currents generated by the rising plumes are visualized with streamline patterns, and the rate of thinning of the remnant layer, as well as the speed of the rising drop or plumes, are discussed.

Description: By using the multiple-scales perturbation method, analytical solutions are obtained for the second-order low-frequency oscillations inside a rectangular harbour excited by incident wave groups. The water depth is a constant. The width of the harbour entrance is of the same order of magnitude as the wavelength of incident carrier (short) waves, but small in comparison with the wavelength of the wave envelope. Because of the modulations in the wave envelope, a second-order long wave is locked in with the wave envelope and propagates with the speed of the group velocity. Outside the harbour, locked long waves also exist in the reflected wave groups, but not in the radiated wave groups. Inside the harbour, the analytical expressions for the locked long waves are obtained. Owing to the discontinuity of the locked long waves across the harbour mouth, second-order free long waves are generated. The free long waves propagate with a speed of (gh)½ inside and outside the harbour. The free long waves inside the harbour may be resonated in a low-frequency range which is relevant to the harbour resonance. © 1990, Cambridge University Press. All rights reserved.

Description: When a coiled tube is rotated about the coil axis, the effects of rotation interact with centrifugal and viscous effects to complicate the flow characteristics beyond those seen in stationary curved ducts. The phenomena encountered are examined for steady, fully developed Newtonian flow in circular tubes of small curvature. The governing equations are solved using orthogonal collocation, and the results presented cover both the nature of the flow and the bifurcation structure. When rotation is in the same direction as the axial flow imposed by a pressure gradient, the flow structure remains similar to that seen in stationary ducts, i.e. with two- or four-vortex secondary flows in addition to the axial flow. There are, however, quantitative changes, which are due to the Coriolis forces resulting from rotation. The bifurcation structure also shows only quantitative changes from that for stationary ducts at all values of Taylor number examined. More complex behaviour is possible when rotation opposes the flow due to the pressure gradient. In particular, the direction of the secondary flow may be reversed at higher rotational strengths, and the mechanism of the flow reversal is explored. The flow reversal occurs smoothly at low Taylor numbers, but at higher rotational strengths a cusp appears in the primary solution branch in the vicinity of the flow reversal.

Description: The deformation of a viscous drop, driven by buoyancy towards a solid surface or a deformable interface, is analysed in the asymptotic limit of small Bond number, for which the deformation becomes important only when the drop is close to the solid surface or interface. Lubrication theory is used to describe the flow in the thin gap between the drop and the solid surface or interface, and boundary-integral theory is used in the fluid phases on either side of the gap. The evolution of the drop shape is traced from a relatively undeformed state until a dimple is formed and a long-time quasi-steady-state pattern is established. A wide range of drop to suspending phase viscosity ratios is examined. It is shown that a dimple is always formed, independently of the viscosity ratio, and that the long-time thinning rates take simple forms as inverse fractional powers of time.

Description: A one-dimensional model is derived for natural convection in a closed loop. The physical model can be reduced to a set of nonlinear ordinary differential equations of the Lorenz type. The model is based on a realistic heat transfer law and also accounts for a non-symmetric arrangement of heat sources and sinks. A nonlinear analysis of these equations is performed as well as experiments to validate the model predictions. Both the experimental and the analytical data show that natural convection in a loop is characterized by strong nonlinear effects. Distinct subcritical regions are observed in addition to a variety of stable steady flow regimes. Thus, in certain ranges of the forcing parameter the flow stability depends significantly on the presence of finite perturbation amplitudes. An absolutely unstable range also exists which is characterized by a chaotic time behaviour of the flow quantities. It is also shown that the steady solutions are subject to an imperfect forward bifurcation if heating of the loop is performed non-symmetrically. In such a case one flow direction is preferred at the onset of convection and, moreover, the corresponding steady solution is more stable than a second, isolated, steady solution. The second solution has the opposite flow direction and is stable only in a relatively small, isolated interval. The preferred steady solution becomes unstable against time-periodic perturbations at a higher value of the forcing parameter. A backward- or a forward-directed bifurcation of the periodic solutions is found depending on the non-symmetry parameter of the system. © 1990, Cambridge University Press. All rights reserved.

Description: A numerical study based on the nonlinear Schrodinger equation, as applied to nonlinear resonant standing waves excited directly by a wavemaker in a rectangular tank, is presented. The stationary solutions of the problem serve as a starting point of the investigation. Bifurcations from a single steady state to multiple stationary solutions are obtained for several values of damping coefficients along the tank and at the wavemaker. The stability of the latter solutions is tested. Limit-cycle or fixed-point solutions are obtained. The results of the numerical study are discussed in connection with experimental data. The necessity of incorporation of dissipation at the wavemaker in the theoretical model in order to obtain qualitative agreement with experiment is demonstrated. © 1990, Cambridge University Press. All rights reserved.

Description: A physical mechanism for the long-wave instability of thin liquid films is presented. We show that the many diverse systems that exhibit this instability can be classified into two large groups. Each group is studied using the model of a thin liquid film with a deformable top surface flowing down a rigid inclined plane. In the first group, the top surface has an imposed stress, while in the other, an imposed velocity. The proposed mechanism shows how the details of the energy transfer from the basic state to the disturbance are handled differently in each of these cases, and how a common growth mechanism produces the unstable motion of the disturbance. © 1990, Cambridge University Press. All rights reserved.

Description: Surface waves superimposed upon a larger-scale flow are blocked at the points where the group velocities balance the convection by the larger-scale flow. Two types of blockage, capillary and gravity, are investigated by using a new multiple-scale technique, in which the short waves are treated linearly and the underlying larger-scale flows are assumed steady but can have a considerably curved surface and uniform vorticity. The technique first provides a uniformly valid second-order ordinary differential equation, from which a consistent uniform asymptotic solution can readily be obtained by using a treatment suggested by the result of Smith (1975) who described the phenomenon of gravity blockage in an unsteady current with finite depth. The corresponding WKBJ solution is also derived as a consistent asymptotic expansion of the uniform solution, which is valid at points away from the blockage point. This solution is obviously represented by a linear combination of the incident and reflected waves, and their amplitudes take explicit forms so that it can be shown that even with a significantly varied effective gravity g’ and constant vorticity, wave action will remain conserved for each wave. Furthermore, from the relative amplitudes of the incident and reflected waves, we clearly demonstrate that the action fluxes carried by the two waves towards and away from the blockage point are equal within the present approximation. The blockage of gravity—capillary waves can occur at the forward slopes of a finite-amplitude dominant wave as suggested by Phillips (1981). The results show that the blocked waves will be reflected as extremely short capillaries and then dissipated rapidly by viscosity. Therefore, for a fixed dominant wave, all wavelets shorter than a limiting wavelength will be suppressed by this process. The minimum wavelengths coexisting with the long waves of various wavelengths and slopes are estimated. © 1990, Cambridge University Press. All rights reserved.

Description: Finite-amplitude solutions of plane Couette flow are discovered. They take a steady three-dimensional form. The solutions are obtained numerically by extending the bifurcation problem of a circular Couette system between co-rotating cylinders with a narrow gap to the case with zero average rotation rate. © 1990, Cambridge University Press. All rights reserved.

Description: A semi-infinite jet flows along a vertical wall in a rotating fluid, with the nose of the intrusion approaching a corner where the wall turns through an obtuse angle 0+180°. The jet separates at the corner and flows into the interior if θ exceeds a critical θC, otherwise part of the jet continues around the corner and flows along the downstream segment of the wall. The separation criterion is computed using an inviscid and piecewise-uniform-vorticity model, with denoting the ratio of the maximum ‘offshore’ to ‘inshore’ vorticity. The separation effect is demonstrated by a laboratory experiment in which a two-dimensional jet flows along the wall from a source. Average velocities are used to estimate s, and to make semi-quantitative comparisons of experimental and theoretical θC. This suggests that the separation mechanism is independent of local viscous forces, although the cumulative effect of lateral eddy stresses in the jet is important in establishing the value of s immediately upstream from the corner. We suggest that our barotropic separation mechanism is relevant to mesoscale oceanic coastal currents. © 1990, Cambridge University Press. All rights reserved.

Description: The linear-eddy model of turbulent mixing represents a spatially developing flow by simulating the time development along a comoving transverse line. Along this line, scalar quantities evolve by molecular diffusion and by randomly occurring spatial rearrangements, representing turbulent convection. The modelling approach, previously applied to homogeneous turbulence and to planar shear layers, is generalized to axisymmetric flows. This formulation captures many features of jet mixing, including differential molecular diffusion effects. A novel experiment involving two unmixed species in the nozzle fluid is proposed and analysed. © 1990, Cambridge University Press. All rights reserved.

Description: The three-dimensional boundary layer on a swept wing can support different types of hydrodynamic instability. Here attention is focused on the so-called ‘spanwise instability’ problem which occurs when the attachment-line boundary layer on the leading edge becomes unstable to Tollmien-Schlichting waves. In order to gain insight into the interactions that are important in that problem a simplified basic state is considered. This simplified flow corresponds to the swept attachment-line boundary layer on an infinite flat plate. The basic flow here is an exact solution of the Navier-Stokes equations and its stability to two-dimensional waves propagating along the attachment line can be considered exactly at finite Reynolds number. This has been done in the linear and weakly nonlinear regimes by Hall, Malik & Poll (1984) and Hall & Malik (1986). Here the corresponding problem is studied for oblique waves and their interaction with two-dimensional waves is investigated. In fact oblique modes cannot be described exactly at finite Reynolds number so it is necessary to make a high-Reynolds-number approximation and use triple-deck theory. It is shown that there are two types of oblique wave which, if excited, cause the destabilization of the two-dimensional mode and the breakdown of the disturbed flow at a finite distance from the leading edge. First a low-frequency mode closely related to the viscous stationary crossflow mode discussed by Hall (1986) and MacKerrell (1987) is a possible cause of breakdown. Secondly a class of oblique wave with frequency comparable with that of the two-dimensional mode is another cause of breakdown. It is shown that the relative importance of the modes depends on the distance from the attachment line. © 1990, Cambridge University Press. All rights reserved.

Description: A complete analysis of the one-dimensional vibratory instability of planar flames of premixed gases propagating in tubes is provided. The driving mechanism results from unsteady coupling between flame structure and acoustic waves through temperature fluctuations. In certain conditions, the strength of such an instability will be proved to be sufficiently strong to produce large-amplitude fluctuations as soon as the flame has travelled a distance of the order of the acoustic wavelength. Stability limits and total amplification of an initial perturbation are computed in the framework of the simple flame mode of a one-step exothermic reaction governed by an Arrhenius law with an activation energy much larger than the thermal energy. Diffusive and thermal effects within the flame are included with a Lewis number different from unity. Damping mechanisms associated with viscous and thermal dissipation at the walls, as well as with loss of acoustic energy by sound radiation from the open end of the tube, are retained. In ordinary conditions, for a reactive mixture with an effective Lewis number close to unity, the predicted instability is weak. In the framework of the simplified flame model used here, islands of strong instabilities are predicted to occur at low Mach numbers for Lewis numbers larger than unity. © 1990, Cambridge University Press. All rights reserved.

Description: Observations of liquid vortex sloshing and Kelvin's equilibrium states were made inside a cylindrical container using a spinning disk near its base. Both steady and periodic free-surface sloshing phenomena were found to take place. During periodic sloshing, the air core sustained shape transformations, assuming an elliptical cross-section at the end, and then collapsed forming a pair of vortices. Kelvin's equilibrium states emerged at lower liquid levels. These were stable within an interval of rotational speeds. The bandwidth of stationary states decreased as the wavenumber (N) increased. For N greater than six, the states appeared critically stable. Between equilibria, unstable transitional regions were found to exist. As the liquid level was decreased, the core shape spectrum shifted towards smaller frequencies.

Description: The stability of two-dimensional thermal convection in an infinite-Prandtl-number fluid layer with zero-stress boundaries is investigated using numerical calculations in three-dimensional rectangles. At low Rayleigh numbers (Ra 〈 20000) calculations of the stability of two-dimensional rolls to cross-roll disturbances are in agreement with the predictions of Bolton & Busse for a fluid with a large but finite Prandtl number. Within the range 2 × 104 〈 Ra ⩽5 × 105, steady rolls with basic wavenumber a 〉 2.22 (aspect ratio 〈 1.41) are stable solutions. Two-dimensional rolls with basic wavenumber a 〈 1.96 (aspect ratio 〉 1.6) are time dependent for Ra 〉 4 × 104. For every case in which the initial condition was a time-dependent large-aspect-ratio roll, two-dimensional convection was found to be unstable to three-dimensional convection. Time-dependent rolls are replaced by either bimodal or knot convection in cases where the horizontal dimensions of the rectangular box are less than twice the depth. The bimodal planforms are steady states for Ra ⩽ 105, but one case at Ra = 5x 105 exhibits time dependence in the form of pulsating knots. Calculations at Ra = 105 in larger domains resulted in fully three-dimensional cellular planforms. A steady-state square planform was obtained in a 2.4 × 2.4 × 1 rectangular box, started from random initial conditions. Calculations in a 3x3x1 box produced steady hexagonal cells when started from random initial conditions, and a rectangular planform when started from a two-dimensional roll. An hexagonal planform started in a 3.5 × 3.5 × 1 box at Ra = 105 exhibited oscillatory time dependence, including boundary-layer instabilities and pulsating plumes. Thus, the stable planform in three-dimensional convection is sensitive to the size of the rectangular domain and the initial conditions. The sensitivity of heat transfer to planform variations is less than 10%. © 1990, Cambridge University Press. All rights reserved.

Description: We experimentally investigate dispersion from a heated line source placed in the central region of a turbulence mixing layer. Recently described by Veeravalli & Warhaft (1989) the mixing layer has no mean shear and consists of gradients in the velocity variance and scale; it is formed from a composite grid of constant solidity from which two distinct velocity scales are formed, one on either side of the stream. Mixing is effected by intermittent turbulent penetration and diffusion. The dispersion measurements were carried out in the convective regime where both plume flapping and fine-scale turbulent mixing play a role, the latter becoming more dominant as the plume evolves. The mean and variance temperature profiles are strongly skewed (with larger tails on the low turbulence side of the flow) in the earlier stages of the plume development. Here, in the convective range, the median and peak of the mean plume are deflected toward the large-scale region. As the flow evolves the profiles become more symmet.rica1 but as the plume enters the turbulent diffusive stage there is evidence that the profiles again became asymmetric but now with longer tails in the high turbulence side of the flow (owing to the higher diffusivity). The temperature variance and heat flux budgets are highly asymmetric but tend to exhibit many of the characteristics of the budget of a line source in decaying homogeneous grid turbulence which is also presented here. However, a distinct region of negative production (counter-gradient heat flux) is found in the temperature variance budget and this is shown to be a consequence of the asymmetry of the transverse velocity probability density function in the mixing layer. Temperature spectra, both of the time series and of the intermittency function, across the plume are described. They are shown to peak at high wavenumbers in the centre and edge of the plume and at lower wavenumbers in the intermediate region. Their form is shown to change as the plume develops fine-scale structure and flapping becomes less important. © 1990, Cambridge University Press. All rights reserved.

Description: The three-dimensional turbulent field of a passive scalar has been mapped quantitatively by obtaining, effectively instantaneously, several closely spaced parallel two-dimensional images; the two-dimensional images themselves have been obtained by laser-induced fluorescence. Turbulent jets and wakes at moderate Reynolds numbers are used as examples. The working fluid is water. The spatial resolution of the measurements is about four Kolmogorov scales. The first contribution of this work concerns the three-dimensional nature of the boundary of the scalar-marked regions (the ‘scalar interface’). It is concluded that interface regions detached from the main body are exceptional occurrences (if at all), and that in spite of the large structure, the randomness associated with small-scale convolutions of the interface are strong enough that any two intersections of it by parallel planes are essentially uncorrelated even if the separation distances are no more than a few Kolmogorov scales. The fractal dimension of the interface is determined directly by box-counting in three dimensions, and the value of 2.35 ± 0.04 is shown to be in good agreement with that previously inferred from two-dimensional sections. This justifies the use of the method of intersections. The second contribution involves the joint statistics of the scalar field and the quantity χ* (or its components), χ* being the appropriate approximation to the scalar ‘dissipation’ field in the inertial–convective range of scales. The third aspect relates to the multifractal scaling properties of the spatial intermittency of χ*; since all three components of χ* have been obtained effectively simultaneously, inferences concerning the scaling properties of the individual components and their sum have been possible. The usefulness of the multifractal approach for describing highly intermittent distributions of χ* and its components is explored by measuring the so-called singularity spectrum (or the f(α)-curve) which quantifies the spatial distribution of various strengths of χ*. Also obtained is a time sequence of two-dimensional images with the temporal resolution on the order of a few Batchelor timescales; this enables us to infer features of temporal intermittency in turbulent flows, and qualitatively the propagation speeds of the scalar interface. Finally, a few issues relating to the resolution effects have been addressed briefly by making point measurements with the spatial and temporal resolutions comparable with the Batchelor lengthscale and the corresponding timescale.

Description: When vortices are embedded in a shearing zonal flow their interactions are changed qualitatively. If the zonal flow’s shear and the vortex’s strength are of the same order and opposite sign, the vortex is pulled into a thin spiral, fragments, and is destroyed in a turn-around time. If the signs are the same, the vortex redistributes its vorticity so that its maximum value is at the centre, and its shape is determined by the ratio of its vorticity to the shear of the surrounding zonal flow. The dynamics depends crucially on the exchange between the self-energy of the vortices and the interaction energy of the zonal flow with the vortices. A numerical example that shows all of these effects is the breakup of a vortex layer: either a single large vortex is formed or successively smaller and more numerous thin filaments of vorticity are created. Two stable vortices are shown to merge if their initial separation in the cross-zonal direction is smaller than a critical distance which is approximately equal the vortices’ radii. The motions of large vortices are constrained by conservation laws, but when the zonal flow is filled with small-scale filaments of vorticity, the large vortices exchange energy with the filaments so that they are no longer constrained by these laws, and their dynamics become richer. Energy is shown to flow from the large vortices to the filaments, and this observation is used to predict the strength of boundary layers and the critical separation distance for vortex merging. © 1990, Cambridge University Press. All rights reserved.

Description: Cavitation inception in a turbulent shear layer was studied at Reynolds numbers up to 2 × 106. Flash photography, high-speed motion pictures and holography were used to study the relation of cavitation inception to the shear-layer turbulent structure. Both spanwise and streamwise vortices were clearly visualized by the cavitation. Cavitation inception consistently occurred in the streamwise vortices and more fully developed cavitation was visible in both structures, with the streamwise cavities typically confined to the braid regions between adjacent spanwise vortices. The strength of the streamwise vortices was estimated using a Rankine vortex model, which showed that their strength was always less than 10 % of that of the spanwise vortices. Measurements of fluctuating pressures were made by holographically monitoring the size of air bubbles injected into the non-cavitating shear flow. The measured pressure fluctuations had positive and negative peaks as high as 3 times the freestream dynamic pressure, sufficient to explain cavitation inception at high values of the inception index. The occurrence of inception in the streamwise vortices of the shear layer, combined with previous reports of velocity dependence of the streamwise vortex strength, may explain the commonly observed Reynolds-number scaling of the cavitation inception index in shear flows. © 1990, Cambridge University Press. All rights reserved.

Description: Experimental investigations were carried out on the coherent structures of turbulent boundary layers in flow with adverse pressure gradient and, in the vicinity of separation, extensive visual observations using hydrogen bubble technique have been performed. In a flow with adverse pressure gradient the size of the structures are larger, therefore more details were observed. By a suitable manipulation of the generation of hydrogen bubble time-lines some new results were obtained in observing plan views near the wall. (1) The long streaks downstream along the interface regions between low-speed and high-speed streaks are continually stretching and their velocity may be greater than that of high-speed streaks, and the hydrogen bubbles in the long streaks generally have a longer life. (2) The x, y-vortices (streamwise) were also observed along the interface regions between high-speed and low-speed streaks. (3) The z-vortices (transverse) were observed at the front of the high-speed regions. © 1990, Cambridge University Press. All rights reserved.

Description: Material line and surface elements transported in a turbulent velocity field increase in length or area at an exponential rate. In this paper we investigate how the stretching rates are related to the statistical properties of the velocity field both analytically and numerically in simple models of turbulence. In a Gaussian model the statistics exhibit time-reversal invariance. We demonstrate that, as pointed out by Kraichnan (1974), this leads to equality of line and area stretching rates. We also construct a model which violates the time-reversal property and splits the values of the rates for lines and surfaces. The sign of the splitting depends on the sign of the time-reversal breakdown. © 1990, Cambridge University Press. All rights reserved.