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  • Articles  (689)
  • Cambridge University Press  (689)
  • 1985-1989
  • 1980-1984  (689)
  • 1925-1929
  • 1983  (689)
  • Physics  (350)
  • Sociology  (339)
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  • Articles  (689)
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  • 1985-1989
  • 1980-1984  (689)
  • 1925-1929
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  • 1
    Publication Date: 1983-12-01
    Description: The effects of imperfect spatial resolution on hot-film and hot-wire measurements of wall-bounded turbulent shear flows were studied. Two hot-film probes of different length were used for measurements of fully developed turbulent channel flow in a water tunnel. In the near-wall region significant effects of spanwise spatial averaging due to finite probe size were found for a probe 32 viscous units long. The maximum turbulence intensity attained a 10% lower value than that for a probe about half as long, and the zero-crossing of the skewness factor was shifted away from the wall. This could be attributed to spatial averaging of narrow low-speed regions. Results for different Reynolds numbers, but with the same sensor length in viscous units, showed that Reynolds-number effects are small, and that much of the reported discrepancies for turbulence measurements in the near-wall region can be ascribed to effects of imperfect spatial resolution. Also the number of events detected with the variable-interval time-averaging (VITA) technique was found to depend strongly on the sensor length, especially for events with short duration.
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  • 2
    Publication Date: 1983-12-01
    Description: The interaction of a rarefaction wave with a gradual monotonic area reduction of finite length in a duct, which produces transmitted and reflected rarefaction waves and other possible rarefaction and shock waves, was studied both analytically and numerically. A quasi-steady flow analysis which is analytical for an inviscid flow of a perfect gas was used first to determine the domains of and boundaries between four different wave patterns that occur at late times, after all local transient disturbances from the interaction process have subsided. These boundaries and the final constant strengths of the transmitted, reflected and other waves are shown as a function of both the incident rarefaction-wave strength and area-reduction ratio, for the case of diatomic gases and air with a specific-heat ratio of 7/5. The random-choice method was then used to solve numerically the conservation equations governing the one-dimensional non-stationary gas flow for many different combinations of rarefaction-wave strengths and area-reduction ratios. These numerical results show clearly how the transmitted, reflected and other waves develop and evolve with time, until they eventually attain constant strengths, in agreement with quasi-steady flow predictions for the asymptotic wave patterns. Note that in all of this work the gas in the area reduction is initially at rest. © 1983, Cambridge University Press. All rights reserved.
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  • 3
    Publication Date: 1983-12-01
    Description: In this paper we present a linear stability analysis for an unbounded, vertically stratified fluid which has compensating horizontal temperature and salinity gradients, so there is no horizontal density gradient. We obtain the most unstable perturbation for given linear horizontal and vertical gradients and calculate the growth rates, the vertical lengthscale of the intrusion and the slope of the intrusion to the horizontal. We show that the system is most unstable to two-dimensional disturbances and that, except for a small region in which the temperature stratification is unstable and the salinity stratification is stable, the most-unstable disturbance is non-oscillatory. We also obtain a solution to the fully nonlinear equations and calculate the fluxes of heat and salt. The nonlinear solution shows that alternating interfaces of salt-finger and diffusive interfaces will eventually appear on the intrusion when the vertical stratifications are both stable. © 1983, Cambridge University Press. All rights reserved.
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  • 4
    Publication Date: 1983-12-01
    Description: The main experimental results of the study of periodic turbulent pipe flow have been described in Part 1 of this report. In this second part, these experimental data are examined in greater detail to understand the effect of imposed oscillation on the flow structure, at moderate to large oscillation frequencies. Data on phase and amplitude and energy spectrum are used to study the effect of the imposed oscillation on the turbulence structure at these interactive frequencies of oscillation. Additional experiments which were performed to study the effect of oscillation frequency on the flow structure are also reported. Based on the present observations as well as on the data from other sources, it is inferred that turbulent shear flows respond very differently from laminar shear flows to imposed unsteadiness. A turbulent Stokes number relevant for characterizing the unsteady turbulent shear flows is identified and used to classify such flows. © 1983, Cambridge University Press. All rights reserved.
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  • 5
    Publication Date: 1983-12-01
    Description: An experimental study has been made of the concept of controlling boundary-layer transition by superimposing in the flow Tollmien-Schlichting waves that are of equal amplitude and antiphased to the disturbances that grow and lead to transition. The cases that have been considered are transition arising from a single-frequency two-dimensional disturbance and transition arising from a nonlinear interaction between two waves of different frequency. A feedback system for controlling transition has also been studied. In each case, both hot-wire surveys and flow visualization have shown that it is possible to delay transition but that the flow cannot be restored completely to its undisturbed state. This appears to be a consequence of interactions between the very weak three-dimensional background disturbances in the flow and the primary two-dimensional waves. The implications of these findings in an implementation of the concept are discussed. © 1983, Cambridge University Press. All rights reserved.
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  • 6
    Publication Date: 1983-12-01
    Description: We consider longshore motion generated within the surf zone by obliquely incident breaking waves, and seek to describe the effect on such motion of variations, caused by wave grouping, in the incident longshore momentum flux. The effects of associated variations in set-up are not considered. We use the linear long-wave equations to describe the motion resulting from the longshore momentum contained in a wave group. This consists of a succession of edge waves which disperse along the beach, and, for the example considered, an eventual steady circulation cell at the position of the wave group. We suggest that such a cell is always likely to be formed if the wave group is sufficiently localized, and that higher-modenumber edge waves are more likely to be excited. We find timescales for the dispersal of the edge waves, and for the decay, due to bottom friction, of the circulation cell: we suggest that the latter may more generally be used, as a timescale for the effect of friction on longshore motion. © 1983, Cambridge University Press. All rights reserved.
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  • 7
    Publication Date: 1983-12-01
    Description: The principal aim of this paper is to derive constitutive equations describing a magnetic fluid. The fluid is modelled as a dilute suspension of small spheroidal magnetic particles in a non-magnetic solute. The conditions for stability of fluid (against coagulation) are discussed and upper and lower bounds for particle sizes are determined. For a stationary fluid, the bulk magnetization is calculated with allowance for particle—particle interactions. The full stress tensor is determined for a flowing fluid that experiences an externally applied magnetic field. Both the flow and field may have arbitrary spatial and time dependences provided only that the lengthscale of spatial variations is large compared with particle dimensions, and that the timescale is long compared with the particle relaxation time due to Brownian motion. These results are applied to shear and pipe flows, where comparison with experiment is made, and to flow induced by rotating magnetic fields. Finally the damping of ultrasound having a characteristic period of the same order as the particle relaxation time is considered. © 1983, Cambridge University Press. All rights reserved.
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  • 8
    Publication Date: 1983-12-01
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  • 9
    Publication Date: 1983-12-01
    Description: The present paper is the first part of a two part report on a detailed investigation of periodic turbulent pipe flow. In this investigation, experimental data on instantaneous velocity and wall shear stress were obtained at a mean Reynolds number of 50000 in a fully developed turbulent pipe flow in which the volumetric flow rate was varied sinusoidally with time around the mean. Two oscillation frequencies at significant levels of flow modulation were studied in detail. The higher of these frequencies was of the order of the turbulent bursting frequency in the flow, and the other can be regarded as an intermediate frequency at which the flow still departed significantly from quasi steady behaviour. While a few similar experiments have been reported in the recent literature, the present study stands out from the others in respect of the flow regimes investigated, the magnitude of flow modulation, the detailed nature of the measurements and most importantly the identification of a relevant parameter to characterize unsteady shear flows. The present paper contains the main experimental results and comparisons of these results with the results of a numerical calculation procedure which employs a well known quasi steady turbulence closure model. The experimental data are used to study the manner in which the time-mean, the ensemble averaged and the random flow properties are influenced by flow oscillation at moderate to high frequencies. In addition, the data are also used to bring out the capability and limitations of quasi steady turbulence modelling in the prediction of unsteady shear flows. A further and more detailed analysis of the experimental data, results of some additional experiments and a discussion on the characterization of turbulent shear flows are provided in Part 2 (Ramaprian & Tu 1983). © 1983, Cambridge University Press. All rights reserved.
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  • 10
    Publication Date: 1983-12-01
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  • 11
    Publication Date: 1983-12-01
    Description: A primary motivation for this work arises from the contradictory results obtained in some recent measurements of the zero-crossing frequency of turbulent fluctuations in shear flows. A systematic study of the various factors involved in zero-crossing measurements shows that the dynamic range of the signal, the discriminator characteristics, filter frequency and noise contamination have a strong bearing on the results obtained. These effects are analysed, and explicit corrections for noise contamination have been worked out. New measurements of the zero-crossing frequency N0have been made for the longitudinal velocity fluctuation in boundary layers and a wake, for wall shear stress in a channel, and for temperature derivatives in a heated boundary layer. All these measurements show that a zero-crossing microscale, defined as Λ = (2πN0)−1is always nearly equal to the well-known Taylor microscale λ (in time). These measurements, as well as a brief analysis, show that even strong departures from Gaussianity do not necessarily yield values appreciably different from unity for the ratio Λ/λ. Further, the variation of N0/N0max across the boundary layer is found to correlate with the familiar wall and outer coordinates; the outer scaling for N0maxis totally inappropriate, and the inner scaling shows only a weak Reynolds-number dependence. It is also found that the distribution of the interval between successive zero-crossings can be approximated by a combination of a lognormal and an exponential, or (if the shortest intervals are ignored) even of two exponentials, one of which characterizes crossings whose duration is of the order of the wall-variable timescale v/U2*while the other characterizes crossings whose duration is of the order of the large-eddy timescale δ/U∞. The significance of these results is discussed, and it is particularly argued that the pulse frequency of Rao, Narasimha & Badri Narayanan (1971) is appreciably less than the zero-crossing rate. © 1983, Cambridge University Press. All rights reserved.
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  • 12
    Publication Date: 1983-12-01
    Description: The long-time t−5/2 behaviour of the angular-velocity autocorrelation function is determined by the diffusion of fluid motion to large distances, from where the particle appears a point singularity. From an examination of this flow, the coefficient of t−5/2 can be related to some effective aspect ratios which describe how the particle rotates in a simple shear flow. © 1983, Cambridge University Press. All rights reserved.
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  • 13
    Publication Date: 1983-12-01
    Description: A generalized energy stability analysis necessarily incorporating charge-diffusion effects is applied to an electrohydrodynamic equilibrium comprising a dielectric liquid confined between two planar electrodes and subjected to an injection of unipolar charge. Generalized energy, kinetic-charge and mixed-type functionals are considered. Using the physical constraint that the sign of space-charge density can never change, it is possible to bound the nonlinear terms in the functional evolution equations. Sufficient conditions to guarantee global monotonic stability in the mean are then derived. In the case of a strong injection of charge the mixed-type functional provides theoretical values of the stability parameter close to the experimental values. Sufficient conditional stability bounds are also obtained for the leading-order diffusion-free equilibrium. © 1983, Cambridge University Press. All rights reserved.
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  • 14
    Publication Date: 1983-11-01
    Description: A circular shear zone is created in a thin layer of fluid. The Kelvin Helmholtz instability induces regular, steady patterns of mvortices. The experimental conditions are such that neither the centrifugal nor the Coriolis forces play a role in the motion. The state of the flow is defined by a Reynolds number, the value of which is controlled by the imposed velocities. The pattern of vortices can be characterized by its wavevector k or by m, the order of its symmetry. As k is quantized, its evolution, due to an increase or a decrease of the controlled stress, leads to transitions between patterns of different m. The transitory states between different symmetries are investigated. The experiments are performed with a soap film which provides a new type of visualization of an air flow. © 1983, Cambridge University Press. All rights reserved.
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  • 15
    Publication Date: 1983-12-01
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  • 16
    Publication Date: 1983-12-01
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  • 17
    Publication Date: 1983-12-01
    Description: Mean drift currents due to spatially periodic surface waves in a viscous rotating fluid are investigated theoretically. The analysis is based on the Lagrangian description of motion. The fluid is homogeneous, the depth is infinite, and there is no continuous energy input at the surface. Owing to viscosity the wave field and the associated mass transport will attenuate in time. For the non-rotating case the present approach yields the time-decaying Stokes drift in a slightly viscous ocean. The analysis shows that the drift velocities are finite everywhere. In a rotating fluid it is found that the effect of viscosity implies a non-zero net mass transport associated with the waves, as opposed to the result of no net transport obtained from inviscid theory (Ursell 1950). © 1983, Cambridge University Press. All rights reserved.
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  • 18
    Publication Date: 1983-12-01
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  • 19
    Publication Date: 1983-12-01
    Description: A set of measurements using arrays of hot-wire anemometers has been performed in the fully developed turbulent wake of a circular cylinder. The data were digitized, recorded on magnetic tape, and processed using the pattern recognition technique described in Part 1 (Mumford 1982), to yield ensemble averages of the stream wise component of the velocity fields of the large eddies in the flow. The results indicate that the large-scale structures in the turbulent wake are predominantly the inclined ‘double-roller’ vortices described by Grant (1958). These eddies consist of two contrarotating roller-like vortices with parallel axes displaced in the spanwise direction and approximately aligned with the direction of the strain associated with the mean velocity gradient. It was found that the structures are often confined to either side of the wake centreplane, rather than extending over the entire thickness of the turbulent region. In addition, eddies of similar type tended to occur in pairs or longer groups with their centres separated in the stream direction. © 1983, Cambridge University Press. All rights reserved.
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  • 20
    Publication Date: 1983-11-01
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  • 21
    Publication Date: 1983-11-01
    Description: The second order transport terms in a monatomic gas, originally derived by Burnett from Boltzmann's equation via the Chapman—Enskog iteration, have the curious property of being dependent on the observer's reference frame. However, frame indifference has long been accepted as an essential property of constitutive equations in continuum mechanics. Various attempts have been made to find errors in the kinetic theory, but these have been countered by physical accounts of the frame dependent terms that are independent of the Chapman Enskog theory. It is shown in this paper that both the Chapman Enskog theory and the physical models are based on an inappropriate definition of the peculiar velocity. The Chapman Enskog theory is easily corrected, and the result is a kinetic theory in harmony with the principle of material frame-indifference. A brief survey of the debate on this topic is presented, and corrected expressions are given for the Burnett terms. © 1983, Cambridge University Press. All rights reserved.
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  • 22
    Publication Date: 1983-11-01
    Description: The effects of ‘crossing trajectories’ and inertia on the dispersion of particles suspended in a field of grid generated turbulence were investigated experimentally. The effect of particle trajectories crossing the trajectories of fluid elements, under the influence of a potential field (usually gravity), is to force the particles from one region of highly correlated flow to another. In this manner, particles lose velocity correlation more rapidly than the corresponding fluid points and as a result disperse less. A homogeneous decaying turbulent field was created behind a square biplanar grid in a wind tunnel. Particles were charged by a corona discharge then passed into the test section through a small plastic tube. A uniform electric field within the test section was used to simulate the effect of gravity, forcing the charged particles out of regions of correlated fluid at a higher than normal rate, therefore inducing the effects of crossing trajectories. Two sizes of glass beads (5 μm and 57 μm diameter) were employed in order to observe inertial effects. Laser Doppler anemometry was used to measure particle mean square displacement, autocorrelation coefficient, and mean square velocity, from which dispersion coefficients were calculated. For the two particle sizes used in the tests, it was found that the particle diffusion coefficient, after a suitably long time from their release, was influenced primarily by the effect of crossing trajectories. Only in the particle mean square velocity was the particle inertia seen to have any effect. The ratio of the particle relaxation time to the Kolmogoroff timescale was found to be a good indicator for the effects of particle inertia. © 1983, Cambridge University Press. All rights reserved.
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  • 23
    Publication Date: 1983-10-01
    Description: We study the existence and the role of solitary waves in the instability of a fluid layer flowing down an inclined plane. The approach presented is fully nonlinear. Solitary waves steady in a moving frame are described by homoclinic trajectories of an associated ordinary differential equation. They are searched numerically for a given value of viscosity and surface tension. Several kinds of solitary waves can exist, characterized by their number n of humps. We investigate the stability of these waves by integrating the initial value problem directly. Solitary waves with more than 1 hump did not appear in the simulation, and moreover a catastrophic behaviour took place for too large a Reynolds number (R ≳ R1) or too large an amplitude, suggesting a finite time singularity. The long term evolution is shown to be a very slow relaxation to a steady state in a moving frame. The relation to the experimental observation of localized wavetrains is also discussed. © 1983, Cambridge University Press. All rights reserved.
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  • 24
    Publication Date: 1983-09-01
    Description: The transport equation for the destruction of temperature fluctuations in a turbulent shear flow is briefly discussed from the point of view of the experimenter’s ability to measure the important terms. The transport equation for only one component of the destruction, the mean-square streamwise temperature derivative, is considered in detail in the case of a steady two-dimensional turbulent shear flow. Measurements of most of the terms in this equation have been made in the self-preserving region of a turbulent plane jet. They indicate that the advection and diffusion terms are negligible compared with the production and dissipation terms. The measured terms are discussed in the context of local isotropy. Mean-square values of second-order derivatives satisfy local isotropy more closely than those of first-order derivatives. © 1983, Cambridge University Press. All rights reserved.
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  • 25
    Publication Date: 1983-09-01
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  • 26
    Publication Date: 1983-09-01
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  • 27
    Publication Date: 1983-09-01
    Description: Measurements of space-time correlations of longitudinal and normal velocity fluctuations and of temperature fluctuations support the existence of counter-rotating spanwise structures appearing alternately on opposite sides of the jet centreline in the self-preserving region of the flow. The frequency of these structures closely satisfies self-preservation. The asymmetric arrangement of the structures is first observed downstream of the position where the jet mixing layers nominally merge but upstream of the onset of self-preservation. Closer to the jet exit, the space—time correlations indicate the existence of spanwise structures that are symmetrical about the centreline. © 1983, Cambridge University Press. All rights reserved.
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  • 28
    Publication Date: 1983-10-01
    Description: We argue that the universality and statistical nature of the deep ocean internal gravity wave spectrum results from a strange attractor in the driven, dissipative internal wave field. To explore this we construct a model which injects energy into the oceanic surface at a constant rate. A two dimensional version of the model is explored analytically and numerically. For the numerical work we restrict our considerations to a few of the longest wavelength modes. This few mode system exhibits bifurcation into limit cycles, period doubling of the limit cycles, and chaotic, non periodic behaviour associated with a strange attractor. In an appendix we present some discussion of the three dimensional version of the model. © 1983, Cambridge University Press. All rights reserved.
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  • 29
    Publication Date: 1983-10-01
    Description: Fully three dimensional surface gravity waves in deep water are investigated in the limit in which the length of the wave crests become long. We describe an analytic solution to fourth order in wave steepness, which matches onto known short crested wave solutions on the one hand and onto the well known two dimensional progressive wave solution on the other. In the progressive wave limit a particular solution in which the wave crests are semi finite is given to sixth order accuracy. These solutions are part of a more general set of solutions which are found from a nonlinear Schrodinger equation. © 1983, Cambridge University Press. All rights reserved.
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  • 30
    Publication Date: 1983-09-01
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  • 31
    Publication Date: 1983-09-01
    Description: Using a ‘ clean ’ jet facility the relationship between the jet flow and its radiation field was studied experimentally in the Mach-number range 0.05 〈 Mj〈 0.20 and a Reynolds-number range 6 × 104〈 ReD〈 2.3 × 105. The various acoustic source parameters such as strength, frequency and Mach number were varied systematically, and the far-field pressure measured simultaneously. On the basis of these measurements the nature of the sources in the initial shear layer could be characterized. The principal results, equally valid for unexcited and excited jets, are as follows: the acoustic sources are not convected but are located within a confined volume fixed with respect to the nozzle even though they are being generated by moving disturbances in the jet; they are associated with the nonlinear saturation of the unstable wave amplitudes of the shear layer occurring at the vortex-pairing locations; the radiation intensity varies nonlinearly with the source strength and is highly directional, exponential in character. © 1983, Cambridge University Press. All rights reserved.
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  • 32
    Publication Date: 1983-09-01
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  • 33
    Publication Date: 1983-09-01
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  • 34
    Publication Date: 1983-09-01
    Description: Density currents in a rotating fluid are produced by releasing a volume of buoyant fluid from a lock at one end of a long rotating channel. Coriolis forces hold the current against one wall. It is observed that the velocity and depth of the nose decrease exponentially in time, implying that the nose can effectively come to a halt at a finite distance from the lock. In reality though, the flow regime eventually changes and a viscous wedge-shaped intrusion continues. The high-Reynolds-number currents contain three-dimensional turbulence a short distance behind the nose, but the influence of rotation causes this to become quasi-two-dimensional further upstream. The intrusion and turbulent motions represent a forcing to the lower layer that produces vortex and wave-like motions which penetrate deep into the lower-layer fluid. It is shown that the exponential decay can be attributed to radiation of momentum by these inertial waves. The width l of the turbulent current varies with distance behind the nose, from 0.6 times the local time-dependent deformation radius at the ‘head’ to l ≈ R0far upstream, where R0is the initial deformation radius in the lock. The nose of the boundary current is unstable, with billows appearing near the tip of the intruding nose and leading to an intermittent breakup of the ‘head ’ structure and oscillations of the nose velocity. These oscillations are rapid, often having frequencies much greater than f (where f = 2Ω is the Coriolis parameter), and, along with the production of the turbulence that is so characteristic of the currents, are attributed to a Kelvin-Helmholtz instability. Rotationally dominated baroclinic waves appear only a very large distance behind the nose. © 1983, Cambridge University Press. All rights reserved.
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  • 35
    Publication Date: 1983-11-01
    Description: Experiments were conducted with three delta wings and two rectangular wings to investigate the evolution of trailing vortices in stratified and unstratified water. The vortex trajectories were determined as a function of the normalized time V0t/b0stratification parameter Nb0/V0and an effective vortex core size re/b0. The results have shown that the vortices rise only to a finite height as they decay gradually at first and rapidly thereafter under the influence of turbulence, sinusoidal instability, and core bursting. The effect of stratification is to reduce the lifespan of vortices and the maximum height attained by them. © 1983, Cambridge University Press. All rights reserved.
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  • 36
    Publication Date: 1983-10-01
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  • 37
    Publication Date: 1983-09-01
    Description: Variations in wave amplitude and steepness across current jets have been described for broad smooth-sided jets. Here, narrow jets are modelled by a top-hat pattern; an approximate solution is found for linear waves, based on conservation of wave action and vertical averaging. The results join remarkably well to those for a broad cosine-shaped jet (cf. McKee 1975). For jet widths less than about a third of a wavelength, there is little change in amplitude; the enhancement predicted by a WKB analysis is suppressed owing to interference with reflections from the far side of the jet. For directional spectra not too different from cos2θ, some suppression occurs near the middle of jets of all scales, owing to exclusion of the glancing wave components by reflection from the near side; this suppression can be significant for jets more than a wavelength wide. For monochromatic waves, maximum amplitudes occur some distance outside the jet owing to interference; the net reflection appears to have a positive phase shift along the near caustic of about ¼cycle. © 1983, Cambridge University Press. All rights reserved.
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  • 38
    Publication Date: 1983-09-01
    Description: In a wind tunnel designed for flow-acoustic measurements, the wall-pressure fluctuations beneath a turbulent boundary layer have been investigated. The measurements were carried out with variously sized pressure transducers (19 ≤ d+≤ 333) and with an array of four small transducers (separation distance Δx+= 75). It is shown that the dimensionless diameter d+= 19 of the transducers is sufficient to resolve the essential structures of the turbulent pressure fluctuations. The power spectrum Φ(ω+) measured with the smallest transducer d+= 19 partly exhibits power-law decay F ~ ω⅞, which has been theoretically predicted for locally isotropic turbulence. By visual analysis and signal averaging in the time domain, pressure structures with high amplitudes could be detected which have the shape of short wavetrains or pulses. Their characteristic frequency and longitudinal wavelength have the mean values ω+= 0.52 and A+= 145 respectively, and their mean convection velocity amounts to uc/u∞= 0.53. It was calculated from the measured probability density that these characteristic structures play an important role, although the probability of their occurrence is low. The sources of these wall-pressure structures can be located in the buffer layer of the boundary layer. © 1983, Cambridge University Press. All rights reserved.
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  • 39
    Publication Date: 1983-08-01
    Description: When a tsunami is incident on a plane shelf, the waveform and amplitude of the reflected wave differ significantly from those of the incident wave, and, when the shelf has the extremely irregular character of real continental shelves, the contrast between the two amplitudes is even greater. Here we quantify these statements and we also give an account of the manner in which the run-up depends on the obliquity and on other parameters characterizing the incident wave. © 1983, Cambridge University Press. All rights reserved.
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  • 40
    Publication Date: 1983-08-01
    Description: In this paper we investigate nonlinear interactions of narrowband, Gaussian-random, inhomogeneous wavetrains. Alber studied the stability of a homogeneous wave spectrum as a function of the width a of the spectrum. For vanishing bandwidth the deterministic results of Benjamin & Feir on the instability of a uniform wavetrain were rediscovered whereas a homogeneous wave spectrum was found to be stable if the bandwidth is sufficiently large. Clearly, a threshold for instability is present, and in this paper we intend to study the long-time behaviour of a slightly unstable modulation by means of a multiple-timescale technique. Two interesting cases are found. For small but finite bandwidth a the amplitude of the unstable modulation shows initially an overshoot, followed by an oscillation around the time-asymptotic value of the amplitude. This oscillation damps owing to phase mixing except for vanishing bandwidth because then the well-known Fermi-Pasta-Ulam recurrence is found. For large bandwidth, however, no overshoot is found since the damping is overwhelming. In both cases the instability is quenched because of a broadening of the spectrum. © 1983, Cambridge University Press. All rights reserved.
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  • 41
    Publication Date: 1983-09-01
    Description: Laser-Doppler velocity measurements were obtained in water between finite rotating disks, with and without throughflow, in four cases: ω1= ω2= 0; ω2/ω1=- 1; ω2/ω1=0; ω2/ω1= 1. The equilibrium flows are unique, and at mid-radius they show a high degree of independence from boundary conditions in r. With one disk rotating and the other stationary, this mid-radius ‘limiting flow ’ is recognized as the Batchelor profile of infinite-disk theory. Other profiles, predicted by this theory to coexist with the Batchelor profile, were neither observed experimentally nor were they calculated numerically by the finite-disk solutions, obtained here via a Galerkin, B-spline formulation. Agreement on velocity between numerical results and experimental data is good at large values of the ratio RQ/Re, where Rq= Q/2πVs Is the throughflow Reynolds number and Re= R22ω/v is the rotational Reynolds number. © 1983, Cambridge University Press. All rights reserved.
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  • 42
    Publication Date: 1983-08-01
    Description: Force measurements were conducted in a pressurized wind tunnel from subcritical up to transcritical Reynolds numbers 2.3 x 104≤ Re ≤7.1 x 106without changing the experimental arrangement. The steady and unsteady forces were measured by means of a piezobalance, which features a high natural frequency, low interferences and a large dynamic range. In the critical Reynolds-number range, two discontinuous transitions were observed, which can be interpreted as bifurcations at two critical Reynolds numbers. In both cases, these transitions are accompanied by critical fluctuations, symmetry breaking (the occurrence of a steady lift) and hysteresis. In addition, both transitions were coupled with a drop of the CDvalue and a jump of the Strouhal number. Similar phenomena were observed in the upper transitional region between the super- and the transcritical Reynolds-number ranges. The transcritical range begins at about Re ≈ 5 x 106, where a narrow-band spectrum is formed with Sr(Re = 7.1 X 106) = 0.29. © 1983, Cambridge University Press. All rights reserved.
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  • 43
    Publication Date: 1983-08-01
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  • 44
    Publication Date: 1983-08-01
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  • 45
    Publication Date: 1983-08-01
    Description: An analysis is given of the initial development of the lift on an aerofoil in inviscid starting flow. It is shown that because of the spiral shape of the vortex sheet shed initially from the trailing edge the lift and drag are both singular at the start of impulsive motion. This result is in contrast with the prediction of finite forces by methods that assume the vortex sheet to be initially planar. The effect of a steady rate of change of incidence following the sudden onset of transverse (heaving) motion of an aerofoil in a steady stream is also discussed. © 1983, Cambridge University Press. All rights reserved.
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  • 46
    Publication Date: 1983-08-01
    Description: An experimental study of the influence of liquid viscosity and viscoelasticity on flow-generated waves on a compliant surface has been conducted in a rotating-disk geometry. Over the entire range of liquid properties studied, each test gave a well-defined critical onset flow velocity above which waves were present and below which no waves were observed. This onset velocity increased with increasing fluid viscosity, and for sufficiently high viscosities the onset occurred when the flow on the disk was laminar rather than turbulent. The effects of liquid viscoelasticity were examined in the turbulent flow using dilute solutions of high-molecular-weight polymers. This type of viscoelasticity had little influence on the onset flow velocity in these circumstances, but did make the wave structure on the surface more regular in appearance than when the liquid was Newtonian. In all cases the wave structure produced a dramatic increase in drag similar to that expected for a rough surface. For the viscoelastic fluid, however, the increase in drag was much less than for a viscous fluid of the same viscosity. © 1983, Cambridge University Press. All rights reserved.
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  • 47
    Publication Date: 1983-08-01
    Description: The output statistics of a laser anemometer operating in a low particle density are discussed. A rigorous derivation is given for the influence of two popular data-handling algorithms on these statistics. In particular it is shown that the measured statistics can differ from those of the flow statistics and from the particle-arrival statistics. The variables that control the statistical regime are derived and quantitative estimates are given for their ranges of influence. The first system discussed is a sample-and-hold system where the output is a piecewise-continuous signal obtained by holding the last processor measurement until a new one is obtained. The second system is one where an attempt is made to store all the measurements for processing, but which contains a rate-limiting device. Because of this device, some measurements may be lost when the particle rate is high. This system is referred to as a saturable system. In both cases it is found that the statistics of the output depend on the product of the mean particle rate and the flow correlation time as well as the flow statistics. The statistics of the saturable system also depend on the ratio of the mean particle rate to the maximum rate at which measurements can be accepted by the system. Because of this, the statistics of both systems depend on the particle density. Attainable conditions are demonstrated, where the output velocity measurement statistics are essentially identical with the flow statistics. © 1983, Cambridge University Press. All rights reserved.
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  • 48
    Publication Date: 1983-08-01
    Description: A two-dimensional Stokes flow close to the line of contact of two touching cylinders or three-dimensional axisymmetric Stokes flow close to the point of contact of two touching bodies is shown in general to separate into infinite sets of eddies with angles of separation from the bodies which tend to 58.61° as the line or point of contact is approached. The flow near the vertex of a conical cusp is shown to be a system of nested toroidal vortices and the separation angles tend to 45.25° as the vertex is approached. Stokes flow between parallel planes or within a circular cylinder is shown in general to separate far from the generating disturbances with cellular eddy structure and separation angles which tend to 58.61° and 45.25° respectively. The mathematical equivalence of the various problems is established. © 1983, Cambridge University Press. All rights reserved.
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  • 49
    Publication Date: 1983-08-01
    Description: The evolution of a weakly nonlinear, weakly dispersive gravity wave in water of depthd over a bottom of gradual slope δ and Chezy friction coefficient Cfis studied. It is found that an initially sinusoidal wave evolves into a periodic sequence of solitary waves with relative amplitude a/d = α1—15δ/4Cfif α1〈 αb, where αbis the relative amplitude above which breaking occurs. This prediction is supported by observations (Wells 1978) of the evolution of swell over mudflats. © 1983, Cambridge University Press. All rights reserved.
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  • 50
    Publication Date: 1983-07-01
    Description: A porous-wavemaker theory is developed to analyse small-amplitude surface waves on water of finite depth, produced by horizontal oscillations of a porous vertical plate. Analytical solutions in closed forms are obtained for the surface-wave profile, the hydrodynamic-pressure distribution and the total force on the wavemaker. The influence of the wave-effect parameter C and the porous-effect parameter G, both being dimensionless, on the surface waves and on the hydrodynamic pressures is discussed in detail. © 1983, Cambridge University Press. All rights reserved.
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  • 51
    Publication Date: 1983-07-01
    Description: A planar liquid layer is bounded below by a rigid plate and above by an interface with a passive gas. A steady shear flow is set up by imposing a temperature gradient along the layer and driving the motion by thermocapillarity. This dynamic state is susceptible to two types of thermal-convective instabilities: (i) stationary longitudinal rolls, which involve the classical Marangoni instability studied by Pearson; and (ii) unsteady hydrothermal waves, which involve a new mechanism of instability deriving its energy from the horizontal temperature gradients. Thermal stability characteristics for liquid layers with and without return-flow profiles are presented as functions of the Prandtl number of the liquid and the Biot number of the interface. Comparisons are made with available experimental observations. © 1983, Cambridge University Press. All rights reserved.
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  • 52
    Publication Date: 1983-07-01
    Description: Corrections to Stokes' law are determined to first order in a/b and a/h for a sphere of radius a in a one-dimensional array of identical spheres having centre-to-centre-spacing b and translating a distance h from a no-slip wall. When h/b is small the drag is greater than that given by Stokes' law; as h/b increases, the drag generally decreases and becomes less than that given by Stokes' law. Stability of the array is examined. Motion along the line of centres is found to be stable, but the other two motions are unstable. The wall is a stabilizing influence when motion is toward the wall and a destabilizing influence when motion is away from the wall. For motion parallel to the wall, the presence of the wall shifts the region of maximum instability to smaller wavelengths. Crowley’s results, which neglect any influence of the wall, are approached for h/b greater than about 5. © 1983, Cambridge University Press. All rights reserved.
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  • 53
    Publication Date: 1983-07-01
    Description: The 2.5-dimensional model of the turbulent field near a wall, proposed by Hatzia-vramidis & Hanratty (1979) and modified by Chapman & Kuhn (1981), has been used to test the subgrid models of Schumann (1973, 1975) and Moin & Kim (1982). The results are disquieting, both trends and orders of magnitude sometimes being seriously in error. It also appears that the contribution of the subgrid energy to the pseudopressure calculated in large-eddy simulations can be large, although this contribution is usually neglected. On the positive side, Leonard's model for the Leonard stress is extremely good, and Schumann’s synthetic boundary condition is also found to be reliable. These results must be taken with a grain of salt, since the tests reported in §5 show that the 2.5-dimensional model cannot reproduce important characteristics of the turbulence in the neighbourhood of y+. = 40. © 1983, Cambridge University Press. All rights reserved.
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  • 54
    Publication Date: 1983-07-01
    Description: A study has been made of how initially planar shocks in air propagate around 90° bends in channels of nearly rectangular cross-section. In shallow bends for which the radius of curvature R is much greater than the radius r of the channel, the shock recovers from a highly curved profile at the start of the bend to regain planarity towards the end of the bend. This occurs on account of the acceleration of the triple point across the channel following its interaction with the expansion waves generated at the convex wall. In sharp bends the shock profiles retain their pronounced curvature for some distance downstream of the bend. At the start of a shallow bend (R/r ≈ 6) the shock at the concave wall, initial Mach number M0, accelerates to Mw. = 1.15M0. and remains at this value until towards the end of the bend it begins to attenuate. At the convex wall, shocks of M0〉1.7 attenuate to Mw= 0.7 M0and propagate at this value for some distance around the bend. In the early stages of a sharper bend (R/r ≈ 3) the shock at the concave wall strengthens to Mw= 1.3M0, remaining at this value for some distance downstream of the bend. At the convex wall the shock decelerates to 0.6M0. Whitham’s (1974) ray theory is shown to predict with reasonable accuracy the Mach numbers of the wall shocks at both surfaces for both bends tested and the range of incident shock velocities used, 1.2 〈 M0〈 3. The agreement between the theory and experimental results is particularly close for stronger shocks propagating along the inner bend. Predictions from 3-shock theory (Courant & Friedrichs 1948) of the Mach number at the outer wall are consistently higher than those from Whitham’s analysis. In turn, the latter tends to slightly overestimate the strength of the wall shock. A model is developed, based on an extension of Whitham’s analysis, and is shown to predict the length of the Mach stem produced by shocks of M0. 〉 2 over the initial stages of the bend. © 1983, Cambridge University Press. All rights reserved.
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  • 55
    Publication Date: 1983-07-01
    Description: This paper discusses the stability of the flow of a low-Prandtl-number liquid contained in a shallow slot with differentially heated vertical endwalls. The effect of thermally insulating boundaries at the top and bottom of the container on wavelength selection is emphasized. Stability calculations indicate that, for Prandtl number Pr in the range 0.015 〈 Pr 〈 0.27, the first perturbations to grow are overstable (oscillatory) longitudinal rolls with axes perpendicular to the endwalls, and with very large cross-stream wavelengths of about 9 to 15 layer depths. Previous studies using thermally conducting boundaries predict critical wavelengths of about three layer depths. The new results are in substantial agreement with an experiment using a differentially heated layer of mercury with aspect ratio (depth/length) 0.047 in both horizontal directions. The implications of the long-wavelength instability for the interpretation of thermal oscillations observed in other smaller-aspect-ratio configurations is discussed. © 1983, Cambridge University Press. All rights reserved.
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  • 56
    Publication Date: 1983-07-01
    Description: We study the primary electroviscous effect in a suspension of spheres when the double layer thickness k−1. is small compared with the particle radius a. The case of a 1–1 symmetric electrolyte is examined using the methods of Dukhin & coworkers (1974), whilst the asymmetric electrolyte is studied along lines similar to those of O'Brien (1983). Sherwood's (1980) asymptotic results for high surface potentials and high Hartmann numbers are extended and complemented. © 1983, Cambridge University Press. All rights reserved.
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  • 57
    Publication Date: 1983-08-01
    Description: The diffraction of obliquely incident surface waves by an asymmetric trench is investigated using linearized potential theory. A numerical solution is constructed by matching particular solutions for each subregion of constant depth along vertical boundaries; the resulting matrix equation is solved numerically. Several cases where the trench-parallel wavenumber component in the incident-wave region exceeds the wavenumber for freely propagating waves in the trench are investigated and are found to result in large reductions in wave transmission; however, reflection is not total owing to the finiteness of the obstacle. Results for one case are compared with data obtained from a small-scale wave-tank experiment. An approximate solution based on plane-wave modes is derived and compared with the numerical solution and, in the long-wave limit, with a previous analytic solution. © 1983, Cambridge University Press. All rights reserved.
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  • 58
    Publication Date: 1983-08-01
    Description: A mathematical representation has been developed for the electromagnetic force field and the fluid-flow field in a coreless induction furnace. The fluid flow field was represented by writing the axisymmetric turbulent Navier-Stokes equations, containing the electromagnetic body-force term. The electromagnetic body force field was calculated by using a technique of mutual inductances. The k-e model was employed for evaluating the turbulent viscosity, and the resultant differential equations were solved numerically. The theoretically predicted velocity fields were in reasonably good agreement with the experimental measurements reported by Hunt & Moore; furthermore, the agreement regarding the turbulence intensities was essentially quantitative. These results indicate the k-e model does provide a good engineering representation of the turbulent recirculating flows occurring in induction furnaces. At this stage it is not clear whether the discrepancies between measurements and the predictions, which were not very great in any case, are attributable either to the model or to the measurement techniques employed. © 1983, Cambridge University Press. All rights reserved.
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  • 59
    Publication Date: 1983-08-01
    Description: Uniform flow in curved, wide, erodible-bed channels is formulated on the basis of the conservation of flux of moment-of-momentum, to obtain relations for the vertical distributions of radial-plane velocity and radial shear stress. The expression for the radial stress exerted on the bed is utilized in a force-equilibrium analysis of the moving bed layer to obtain relations for the average transverse slope of the bed and for the radial bed profile. The reduction of primary bed shear stress due to the net radial transport of streamwise momentum toward the outer (concave) bank is then calculated, by introducing the derived expressions for the velocity components into the momentum equation for the primary-flow direction. It is found that the stress reductions in deep, narrow channels can exceed 50%. Bed profiles and velocity distributions measured in natural and laboratory streams are found to be in good conformity with those calculated from this moment-based theory.
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  • 60
    Publication Date: 1983-08-01
    Description: The effect of a small amount of Brownian diffusion on shear-induced coagulation of spherical particles has been calculated. This has been accomplished by considering the binary collision process between a test sphere and identical spheres interacting with the test sphere through induced-dipole attraction, electrostatic repulsion and hydrodynamically induced forces. The effect of diffusion is found by means of an expansion in inverse Péclet number. Specific calculations were performed for uniaxial extension and for laminar shear flow. It is found that Brownian diffusion, the effect of which is nonlinearly coupled with flow type and strength, can act to increase or decrease the coagulation rate. © 1983, Cambridge University Press. All rights reserved.
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  • 61
    Publication Date: 1983-08-01
    Description: The time-dependent evolution of sheared Rossby waves starting from an initial disturbance is studied for the simple case in which the shear is uniform. The uniform-shear assumption allows explicit solutions to be obtained which are useful in addressing the issue of the long-time asymptotic approach to normal modes and in assessing the relative importance of viscosity, nonlinearity and time-dependence in the evolution of Rossby waves in the presence of critical layers. © 1983, Cambridge University Press. All rights reserved.
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  • 62
    Publication Date: 1983-08-01
    Description: In this analysis, the translation of a liquid drop experiencing a strong non-uniform radial velocity has been investigated. The situation arises when a moving liquid drop experiences condensation, evaporation or material decomposition at the surface. By simultaneously treating the flow fields inside and outside the drop, we have obtained physical results relevant to the problem. The magnitude of the radial velocity is allowed to be very large, but the drop motion is restricted to slow translation. The solution to the problem has been developed by considering a uniform radial flow with the translatory motion introduced as a perturbation. The role played by the inertial terms due to the strong radial field has been clearly delineated. The study has revealed several interesting features. An inward normal velocity on a slowly moving drop increases the drag. An increasing outward normal velocity decreases the drag up to a minimum beyond which it increases. The total drag force not only consists of contributions from the viscous and the form drags but also from the momentum transport at the interface. Since the liquid drop admits a non-zero tangential velocity, the tangential momentum convected by the radial velocity forms a part of this drag force. The circulation inside the drop decreases (increases) with an outward (inward) normal velocity. A sufficiently large non-uniform outward velocity causes the circulation to reverse. In the limit of the internal viscosity becoming infinite, our analysis collapses to the simple case of a translating rigid sphere experiencing a large non-uniform radial velocity. By letting the radial velocity become vanishingly small the Stokes-flow solution is recovered. An important contribution of the present study is the identification of a new singularity in the flow description. It accounts for both the inertial and the viscous forces and displays Stokeslet-like characteristics at infinity. © 1983, Cambridge University Press. All rights reserved.
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  • 63
    Publication Date: 1983-08-01
    Description: This paper describes a laboratory experiment designed to compare measurements with published theoretical ideas of the mixed-layer growth of a two-layer system in which the turbulence is induced by an oscillating grid. Experimental results show excellent agreement with an earlier theory by one of us (Long), in which the mixed-layer depth D* measured from a virtual origin is given by $D_{*}sim V_0^{-frac{7}{11}}K^{frac{9}{11}}t^{frac{2}{11}}$, where K is action, t is time and V0 is a characteristic velocity of the problem. The experiments also verify Long's theoretical entrainment relation E = α2Ri−7/4, where E is the entrainment coefficient and $Ri = D^3_{*}Delta b/K^2$, and Δb is the buoyancy difference between the two layers. The interfacial-layer thickness was observed to be proportional to the depth of the mixed layer, as also predicted by Long. After a certain depth, the entrainment law tends to deviate from Long's theory. The deviation may be due to wall effects.
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  • 64
    Publication Date: 1983-08-01
    Description: Experiments were conducted to determine the effective diffusivity for axial transport through a tube of circular cross-section of a contaminant gas in oscillatory flow. Results were compared with the theoretical predictions of Watson (1983) and found to be in excellent agreement. The experiments differ from the theoretical situation in that the oscillations are superimposed upon a steady flow due to a constant infusion of tracer gas, and a buoyancy-induced flow associated with spatial variations in gas density. The influence of both artifacts is found to be negligible.
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  • 65
    Publication Date: 1983-08-01
    Description: A novel, digital, hot-wire anemometer technique for the simultaneous measurement of the instantaneous streamwise and lateral velocity fields in high-intensity turbulent flows is discussed. It involves the use of a three-wire probe comprising two 45° slanted hot wires and a normal hot wire. A comprehensive and systematic examination of several factors that can affect the fidelity of the streamwise and lateral velocity waveforms is developed to assess the performance of the new technique as well as hot-wire systems generally. These factors are: (i) rectification, which stems from the inherent insensitivity of hot wires to the direction of the instantaneous (total) velocity vector in a turbulent flow; (ii) spanwise velocity fluctuations; (iii) axial cooling of hot wires; (iv) unpredictable variations in one of four hot-wire calibration parameters; (v) random hot-wire calibration errors; (vi) spanwise separation of the hot wires. Relevant hot-wire anemometer-response equations relating instantaneous anemometer output voltages to instantaneous flow velocities were established on the basis of extensive voltage-velocity calibration data pertaining to hot wires orientated with respect to the calibration flow velocity at various yaw and pitch angles ranging from 0° to 90°. Simulated Gaussian (streamwise, lateral and spanwise) velocity fields appropriate to flows with turbulence intensity levels varying between 5 and 80% and Reynolds shear-stress coefficients varying between 0.1 and 0.5 were generated by means of a digital computer, and the associated anemometer-voltage signals computed in accordance with the response equations subject to different combinations of the first four of the aforementioned factors. In order to take into account the effects of the last two factors, viz calibration errors and spanwise wire separation, uncorrelated Gaussian ‘noise’ fluctuations were superimposed on the above voltage signals. Estimates of the known (simulated) streamwise and lateral velocity signals were then determined by simultaneous solution of (a) the actual instantaneous response equations, (b) approximate versions of them, and (c) linearized versions of them. The results indicate that reasonably accurate estimates of velocity signals from a turbulent flow can be obtained by means of conventional hot-wire anemometer techniques – which assume that anemometer voltage fluctuations are linear functions of corresponding velocity fluctuations – only if the turbulent intensity level of the flow does not exceed about 20%. In marked contrast, the 3-wire anemometer technique introduced here can be used to measure streamwise and lateral velocity signals simultaneously with a high degree of accuracy for turbulence-intensity levels of up to 40%. In addition, this technique is capable of yielding high-fidelity streamwise velocity waveforms for levels in excess of 70%.
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  • 66
    Publication Date: 1983-07-01
    Description: Two-dimensional flow past a cylindrical body of arbitrary profile at small Reynolds numbers is studied theoretically. The asymptotic flow field at large distances from an immersed body is shown to depend only upon the force acting on the cylinder. This universal field is determined by solving the Navier-Stokes equation numerically. The result enables us to evaluate the force acting on the body as a function of the flow Reynolds number. A detailed calculation is made of the drag coefficients of a circular cylinder and a flat plate. Results compare favourably with existing experimental and numerical data. © 1983, Cambridge University Press. All rights reserved.
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  • 67
    Publication Date: 1983-08-01
    Description: Previous experimental studies are reviewed and those whose data are deemed reliable are identified. New experiments at larger scale are described and the results are reported. These are combined with the reliable previous studies to form a data set covering heights from 3.66 to 50m and gasflow rates from 0.0002 to 0.59 normal m3/s. These wide-ranging data are combined with an integral theory for bubble plumes to determine functional relationships between local plume properties and the entrainment coefficient and the fraction of the momentum flux that is carried in the turbulent velocity fluctuations. These relationships together with the integral theory provide a set of equations that are suitable for numerical solution for the mean flow properties of any round bubble plume. Examples of the numerical solutions are presented and a comparison of one of these with existing experimental data is given. The relationships between the local plume properties and the entrainment coefficient and the momentum flux carried by the turbulence are interpreted to provide a qualitative understanding of the parameters involved and their influences on the plume. © 1983, Cambridge University Press. All rights reserved.
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  • 68
    Publication Date: 1983-07-01
    Description: Hamilton's principle of mechanics has special advantages as the beginning point for approximations. First, it is extremely succinct. Secondly, it easily accommodates moving disconnecting fluid boundaries. Thirdly, approximations-however strong-that maintain the symmetries of the Hamiltonian will automatically preserve the corresponding conservation laws. For example, Hamilton’s principle allows useful analytical and numerical approximations to the equations governing the motion of a homogeneous rotating fluid with free boundaries. © 1983, Cambridge University Press. All rights reserved.
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  • 69
    Publication Date: 1983-06-01
    Description: This paper reports a fundamental study of the fluid dynamics inside a triangular (attic-shaped) enclosure with cold upper wall and warm horizontal bottom wall. The study was undertaken in three distinct parts. In the first part, the flow and temperature fields in the cavity are determined theoretically on the basis of an asymptotic analysis valid for shallow spaces (H/L→0, where H and L are the attic height and length). It is shown that in the H/L→0 limit the circulation consists of a single elongated cell driven by the cold upper wall. The net heat transfer in this limit is dominated by pure conduction. In the second part of the study, the transient behaviour of the attic fluid is examined, based on a scaling analysis. The transient phenomenon begins with the sudden cooling of the upper sloped wall. It is shown that both walls develop thermal and viscous layers whose thicknesses increase towards steady-state values. The criterion for the existence of distinct thermal layers in the steady state is (H/L)1/2. RaH−1/4. 〉 1, where RaH. is the Rayleigh number based on attic height. The corresponding criterion for distinct viscous wall jets is (H/L)1/2. RaH1/4. Pr−1/2. 〉 1, where Pr is the Prandtl number. The third phase of this study focused on a complete sequence of transient numerical simulations covering the ranges H/L = 0.2, 0.4, 1; RaH/Pr = 10, 103, 105; Pr = 0.72, 6. The numerical experiments verify the flow features described theoretically in the first two parts of the study. The effect of thermal convection on the net heat transfer between the bottom and top walls is illustrated numerically. Finally, the transient numerical experiments show that in the present parametric domain the single-cell circulation pattern is stable with respect to the Benard instability expected in fluid layers heated from below. © 1983, Cambridge University Press. All rights reserved.
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  • 70
    Publication Date: 1983-06-01
    Description: Measurements of a steady free-stream, nominally two-dimensional, separating turbulent boundary layer have been reported in earlier parts of this work. Here measurements are reported that show the effects of frequency on sinusoidal unsteadiness of the free-stream velocity on this separating turbulent boundary layer at reduced frequencies of 0.61 and 0.90. The ratio of oscillation amplitude to mean velocity is about 1/3 for each flow. Upstream of flow detachment, hot-wire anemometer measurements were obtained. A surface hot-wire anemometer was used to measure the phase-averaged skin friction. Measurements in the detached-flow zone of phase-averaged velocities and turbulence quantities were obtained with a directionally sensitive laser anemometer. The fraction of time that the flow moves downstream was measured by the LDV and by a thermal flow-direction probe. Upstream of any flow reversal or backflow, each flow behaves in a quasisteady manner, i.e. the phase-averaged flow is described by the steady free-stream flow structure. The semilogarithmic law-of-the-wall velocity profiles applies at each phase of the cycle. The Perry & Schofield (1973) velocity-profile correlations fit the mean and ensemble-averaged velocity profiles near detachment. After the beginning of detachment, large amplitude and phase variations develop through each flow. Unsteady effects produce hysteresis in relationships between flow parameters. As the free-stream velocity during a cycle begins to increase, the detached shear layer decreases in thickness, and the fraction of time [formula omitted] that the flow moves downstream increases as backflow fluid is washed downstream. As the free-stream velocity nears the maximum value in a cycle, the increasingly adverse pressure gradient causes progressively greater near-wall backflow at downstream locations while [formula omitted] remains high at the upstream part of the detached flow. After the free-stream velocity begins to decelerate, the detached shear layer grows in thickness, and the location where flow reversal begins moves upstream. This cycle is repeated as the free-stream velocity again increases. In both unsteady flows, the ensemble-averaged detached-flow velocity profiles agree with steady free-stream profiles for the same [formula omitted] value near the wall when [formula omitted]. However, the reduced-frequency k = 0.90 flow has much larger hysteresis in ensemble-averaged velocity profile shapes when [formula omitted]. Larger and negative values of the profile shape factor Ĥ occur for this flow during phases when the non-dimensional backflow is greater and [formula omitted]. © 1983, Cambridge University Press. All rights reserved.
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  • 71
    Publication Date: 1983-06-01
    Description: The nonlinear time-dependent adjustment of a homogeneous rotating-channel flow to the sudden obtrusion of an obstacle is studied. Solutions are obtained using a Lax-Wendroff numerical scheme which allows rotating breaking bores and jumps to form and be maintained. The flow upstream of the obstacle is found to be completely blocked, partially blocked (and hydraulically controlled), or unobstructed depending upon the height of the obstacle. Partial blockage is accomplished through the excitation of a combination of nonlinear Kelvin waves, some of which steepen into interfacial shocks. Riemann invariants for the Kelvin waves are found, and jump conditions on mass, momentum and potential vorticity for the shocks are discussed. The shocks are surrounded by dispersive regions of Rossby deformation scale, and the potential vorticity of passing fluid is altered at a rate proportional to the differential rate of energy dissipation along the line of breakage. For the special case of initially uniform potential vorticity the asymptotic state is found as a function of the initial conditions. © 1983, Cambridge University Press. All rights reserved.
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  • 72
    Publication Date: 1983-05-01
    Description: Experiments are performed on steady and impulsively started flow in an approximately two-dimensional closed channel, with one wall locally indented. In plan the indentation is a long trapezium which halves the channel width; the inclination of the sloping walls is approximately 5.7°, and these tapered sections merge smoothly into the narrowest section via rounded corners. The Reynolds number Re = a0u0/v (ao= unindented channel width, u0= steady mean velocity in the unindented channel) lies in the range 300 ^ Re ^ 1800. In steady flow, flow visualization reveals that separation occurs on the lee slope of the indentation, at a distance downstream of the convex corner which decreases (tending to a non-zero value) as Re increases. There is no upstream separation, and there is some evidence of three-dimensionality of the flow in the downstream separated eddy. Pressure measurements agree qualitatively but not quantitatively with theoretical predictions. Unsteady flow visualization reveals that, as in external flow, wall-shear reversal occurs over much of the lee slope (at dimensionless time τ = ū0t/a0≈ 4) before there is any evidence of severe boundary-layer thickening and breakaway. Then, at τ ≈ 5.5, a separated eddy develops, and its nose moves gradually upstream from the downstream end of the indentation to its eventual (τ ≈ 75) steady-state position on the lee slope. At about the same time as the wall-shear reversal, wavy vortices appear at the edge of the boundary layer on both walls of the channel, and (for Re 〈 750) subsequently disappear again; these are interpreted as manifestations of inflection-point instability and not as intrinsic aspects of boundary-layer separation. Pressure measurements are made to investigate the discrepancy between the actual pressure drop across the lee slope and that predicted on the assumption that energy dissipation is quasi-steady. This discrepancy has a maximum value of approximately 1.5ρū20 (ρ = fluid density), and decays to zero by the time τ ≈ 7. © 1983, Cambridge University Press. All rights reserved.
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  • 73
    Publication Date: 1983-05-01
    Description: An analytical solution of a system of linearized equations for a gas-particle mixture is obtained for steady periodic motions. A finite volume fraction of particles and a continuous distribution of particle sizes are taken into consideration. It is shown that the effect of a continuous distribution of particle radii on the acoustic motions of a dusty gas is incorporated through only four integral quantities containing the relaxation times of the particle velocity and temperature, integrated over all particle sizes. This solution is applied to the problem of acoustic reflection, absorption, and transmission by a screen of dusty gas. © 1983, Cambridge University Press. All rights reserved.
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  • 74
    Publication Date: 1983-05-01
    Description: A general expression is obtained for the longitudinal dispersion coefficient for a passive contaminant in a varying channel. This expression reveals the upstream memory character of the dispersion coefficient. Simple examples are used to illustrate the effects of: A sudden change in breadth, centrifugally driven secondary flows, and changes in the depth profile. © 1983, Cambridge University Press. All rights reserved.
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  • 75
    Publication Date: 1983-05-01
    Description: A function ϕ is derived which is constant along the orthogonal trajectories of streamlines in two-dimensional flow. In irrotational flows, ϕ reduces to the velocity potential. The pair of functions ϕ and Ψ, where Ψ is the stream function, are used to define a coordinate system in rotational fluid flows. Tensor methods are used to transform the equations of motion of a turbulent fluid and the equations for second moments of turbulent fluctuations to this coordinate system. Explicit extra terms appear in the transformed equations embodying the effects of streamline curvature and mean flow acceleration. These extra terms are characterized by two lengthscales which arise naturally from the transformation: the local radius of curvature of the streamline and the ‘e-folding’ distance of the mean streamwise velocity. © 1983, Cambridge University Press. All rights reserved.
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  • 76
    Publication Date: 1983-07-01
    Description: The temporal and spatial evolution of large-scale modulations of weakly nonlinear edge waves on a uniformly sloping beach is studied using the full water-wave formulation for beach angles α=π/2N. Equations governing the evolution of envelopes of edge waves, excited by resonant interactions with incident wavetrains, are derived. It is deduced that a uniform train of free periodic edge waves is always unstable to large-scale variations, so that envelope solitons will develop; the resulting three-dimensional solitons are described in detail. In addition, it is shown that steady-state standing subharmonic edge waves, excited by incident wavetrains on a long, mildly sloping beach, can be unstable to large-scale modulations. The possible physical significance of these findings is discussed. © 1983, Cambridge University Press. All rights reserved.
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  • 77
    Publication Date: 1983-07-01
    Description: The critical Taylor number, phenomena accompanying the transition to turbulence, and the cellular structure of Taylor-Görtler vortex in the flow between two concentric spheres, of which the inner one is rotating and the outer is stationary, are investigated using three kinds of flow-visualization technique. The critical Taylor number generally increases with the ratio β of clearance to inner-sphere radius. For β ≤ 0.08, the critical Taylor number in spherical Couette flow is smaller than in circular Couette flow, but vice versa for β 〉 0.08. A pair of toroidal Taylor-Görtler vortices occurs first around the equator at the critical Reynolds number Rec. (or critical Taylor number Tc). More Taylor-Görtler vortices are added with increasing Reynolds number Re. After reaching the maximum number of vortex cells, as Reis increased, the number of vortex cells decreases along with the various transition phenomena of Taylor-Görtler vortex flow, and the vortex finally disappears for very large Re, where the turbulent basic flow is developed. The instability mode of Taylor-Görtler vortex flow depends on both ft and Re. The vortex flows encountered as Reis increased are toroidal, spiral, wavy, oscillating (quasiperiodic), chaotic and turbulent Taylor-Görtler vortex flows. Fourteen different flow regimes can be observed through the transition from the laminar basic flow to the turbulent basic flow. The number of toroidal and/or spiral cells and the location of toroidal and spiral cells are discussed as a means to clarify the spatial organization of the vortex. Toroidal cells are stationary. However, spiral cells move in relation to the rotating inner sphere, but in the reverse direction of its rotation and at about half its speed. The spiral vortices number about six, and the spiral angle is 2-10°. © 1983, Cambridge University Press. All rights reserved.
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  • 78
    Publication Date: 1983-07-01
    Description: Three modes of instabilities in the slit-jet flow field are recognized. Additional evidence for the universality of the Strouhal number for the second mode ST. =fw/U0. = 0.43 and additional information on the wavelength (A) between, and convection speed uc. of the symmetrically placed, large-scale motions that result from this instability are presented. Specifically λ/w≈1.2 and uc/U0≈ 0.51. The third instability mode is initiated at a Reynolds number U0w/v of approximately 1600; this instability results in a loss of the regular pattern associated with the large-scale motions. © 1983, Cambridge University Press. All rights reserved.
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  • 79
    Publication Date: 1983-07-01
    Description: The linear stability of the stationary Ekman-layer flow near a plane boundary is considered. Analytical formulas for the eigenfunctions are derived by a spectral analysis. Standard optimization algorithms are used to calculate critical points, maximum growth rates and neutral-stability curves. The new approach provides a better basis for both a linear and a nonlinear stability analysis than the well-known methods have done. The method may also be applied to other boundary-layer problems. © 1983, Cambridge University Press. All rights reserved.
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  • 80
    Publication Date: 1983-05-01
    Description: It is shown that the advection—diffusion equation for contaminant dispersion in water of variable depth admits of an inverse approach in which the stochastic mean concentration at a fixed sensitive location is calculated for arbitrary discharge sites. A ray method is used to obtain simple approximate solutions for the inverse problem when the sensitive location is situated at the shoreline. This makes explicit the considerable improvements in shoreline pollution levels which can be gained by siting effluent outfalls further away from the shore. © 1983, Cambridge University Press. All rights reserved.
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  • 81
    Publication Date: 1983-05-01
    Description: The growth of Gortler vortices in boundary layers on concave walls is investigated. It is shown that for vortices of wavelength comparable to the boundary-layer thickness the appropriate linear stability equations cannot be reduced to ordinary differential equations. The partial differential equations governing the linear stability of the flow are solved numerically, and neutral stability is defined by the condition that a dimensionless energy function associated with the flow should have a maximum or minimum when plotted as a function of the downstream variable X. The position of neutral stability is found to depend on how and where the boundary layer is perturbed, so that the concept of a unique neutral curve so familiar in hydrodynamic-stability theory is not tenable in the Gortler problem, except for asymptotically small wavelengths. The results obtained are compared with previous parallel-flow theories and the small-wavelength asymptotic results of Hall (1982a, b), which are found to be reasonably accurate even for moderate values of the wavelength. The parallel-flow theories of the growth of Görtler vortices are found to be irrelevant except for the small-wavelength limit. The main deficiency of the parallel-flow theories is shown to arise from the inability of any ordinary differential approximation to the full partial differential stability equations to describe adequately the decay of the vortex at the edge of the boundary layer. This deficiency becomes intensified as the wavelength of the vortices increases and is the cause of the wide spread of the neutral curves predicted by parallel-flow theories. It is found that for a wall of constant radius of curvature a given vortex imposed on the flow can grow for at most a finite range of values of X. This result is entirely consistent with, and is explicable by the asymptotic results of, Hall (1982a). © 1983, Cambridge University Press. All rights reserved.
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  • 82
    Publication Date: 1983-05-01
    Description: When the flow over a submerged, round, upright cylinder, situated in a large ocean, is forced by a train of plane waves, linear theory (Yamamuro 1981) shows that the response can be abnormally large for certain forcing frequencies. The aim of this paper is to present a weakly nonlinear theory, where wave interactions, arising from the quadratic terms in the free-surfaee boundary conditions, can yield abnormally large responses. A specific interaction will be considered between a flow at a subharmonic frequency and a flow at the driving frequency. The reason for considering such an interaction derived from a consideration of some experimental results of Barnard, Pritchard & Provis (1981). © 1983, Cambridge University Press. All rights reserved.
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  • 83
    Publication Date: 1983-05-01
    Description: The flow in a partially filled, strongly rotating cylinder with a differentially rotating endcap was studied both experimentally and numerically. The cylindrical container was mounted with a vertical axis of rotation, partially filled with an incompressible fluid, and rotated at a sufficiently high angular velocity that the fluid formed a film of essentially uniform thickness on the sidewall of the container. An axial circulation in this fluid film was induced by the differential rotation of one of the container endcaps. A laser-Doppler velocimeter was used to measure the axial and azimuthal velocity components. The experimental results were compared with a finite-difference model of the flow, and the agreement between the two was good. Boundary layers of thickness proportional to E⅓, where E — v/ΩL2 is the Ekman number, are found both at the lateral wall and at the vertical free surface. The existence of an E⅓ boundary layer along the free surface is due to the invariant structure of the E1/2 Ekman layers on the horizontal surfaces with respect to a free surface. The radial transport in the Ekman layers of a partially filled rotating cylinder is essentially the same as that in a completely filled container. The axial transport, which in a completely filled container would have occurred in the volume now occupied by an empty core, is instead confined to a thin boundary layer along the free surface. © 1983, Cambridge University Press. All rights reserved.
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  • 84
    Publication Date: 1983-05-01
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  • 85
  • 86
    Publication Date: 1983-05-01
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  • 87
    Publication Date: 1983-05-01
    Description: Free-surface and internal stationary waves in a meandering stream are treated, and analytical solutions given. It is shown that for each category there is an infinite number of Froude numbers, depending on the wavenumber of the meander, at which resonance occurs, and the amplitude of one of the wave components becomes infinite, according to the linear theory. These critical Froude numbers are interpreted physically. Furthermore, variable depth is treated for the case of free-surface waves, and in this treatment it is shown, incidentally, how the eigenvalues of a singular differential equation can be found under the requirement that the eigenfunction be non-singular. Finally, an attempt is made to explain the self-induced, non-stationary waves in water flowing between corrugated vertical walls, found by Binnie (1960), by an instability mechanism proposed by Yih (1976). There is strong evidence that this mechanism is at work, at least when a sloshing mode is involved in the wave-triad interaction. © 1983, Cambridge University Press. All rights reserved.
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  • 88
    Publication Date: 1983-05-01
    Description: Liquids held by surface tension forces can bridge the gap between two solid bodies placed not too far apart from each other. The equilibrium conditions and stability criteria for static, cylindrical liquid bridges are well known. However, the behaviour of an unstable liquid bridge, regarding both its transition toward breaking and the resulting configuration, is a matter for discussion. The dynamical problem of axisymmetric rupture of a long liquid bridge anchored at two equal coaxial disks is treated in this paper through the adoption of one-dimensional theories which are widely used in capillary jet problems. © 1983, Cambridge University Press. All rights reserved.
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  • 89
    Publication Date: 1983-05-01
    Description: A numerical study is conducted on the pressure-driven laminar flow of an incompressible viscous fluid through a rectangular channel subjected to a spanwise rotation. The full nonlinear time-dependent Navier-Stokes equations are solved by a finite-difference technique for various rotation rates and Reynolds numbers in the laminar regime. At weak rotation rates, a double-vortex secondary flow appears in the transverse planes of the channel. For more rapid rotation rates, an instability occurs in the form of longitudinal roll cells in the interior of the channel. Further increases in the rotation rate leads to a restabilization of the flow to a Taylor—Proudman regime. It is found that the roll-cell and Taylor—Proudman regimes lead to a substantial distortion of the axial-velocity profiles. The specific numerical results obtained are shown to be in excellent agreement with previously obtained experimental measurements and theoretical predictions. © 1983, Cambridge University Press. All rights reserved.
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  • 90
    Publication Date: 1983-06-01
    Description: The equilibrium configurations of a liquid spreading on a rough solid surface are derived by making expansions in terms of the characteristic slope e of the surface roughness, which is assumed to be very small. It is also assumed that the microscopic contact angle is a constant and that the liquid-air interface is planar at large distances from the contact line. Expressions for the value of the macroscopic contact angle and a discussion of the existence of contact-angle hysteresis and of stick-jump behaviour of the contact line are given for (i) surfaces with parallel grooves, (ii) surfaces with periodicity in two perpendicular directions and (iii) general non-period surfaces. © 1983, Cambridge University Press. All rights reserved.
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  • 91
    Publication Date: 1983-05-01
    Description: The occurrence of new unstable modes of quasigeostrophic baroclinic oscillation of rotating stratified shear flow over a wavy bottom is examined. To obtain a tractable mathematical problem, the bottom topography is considered as a perturbation modifying the oscillations. It is found that combinations of a top-intensified and a bottom-intensified Eady mode, each stable without topography, can be destabilized by topography if certain resonant conditions are met. These are that (i) the two modes possess the same wavefrequency, and (ii) topography possesses a wavenumber c bridging the gap between the wavenumbers of the modes a, b, i.e. c = a — b. Growth rate of this instability (called type A) is proportional to the amplitude of the topographic component. There are two special cases: (i) when one of the basic modes is a marginally neutral mode - according to the classical analysis without topography - the instability is stronger (type M) with growth rate proportional to the ⅔-power of topographic amplitude; (ii) when both modes are marginally neutral the instability is even stronger (type M2) with growth rate proportional to the square root of topographic amplitude. These topographic instabilities, like classical baroclinic instability, draw their energy from the available potential by transporting buoyancy down the mean gradient associated with the geostrophic shear flow. © 1983, Cambridge University Press. All rights reserved.
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  • 92
    Publication Date: 1983-05-01
    Description: The transition process of mechanically generated regular waves into wind waves is investigated in a wind-wave tunnel. Modulations of characteristic quantities of the waves are examined in both space and time using wave-gauge arrays. The transition begins with the occurrence of wave breaking, and it is associated with the following two processes: (i) the irregularization, i.e. the generation and amplification of a random modulation whose wave height and period are in phase; and (ii) the frequency shift to the lower side by the mutual coalescence of waves through the amplification of the modulation, the coalescence occurring at the troughs of the period modulation. The modulational properties under the effect of wind with wave breaking are thus in part different from the theoretical prediction of modulational instability of a freely travelling wavetrain. It is concluded that the mechanism of the transition is the modulational instability coupled with the wind effects. © 1983, Cambridge University Press. All rights reserved.
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  • 93
    Publication Date: 1983-05-01
    Description: Exact solutions of the equations of motion for an inviscid fluid are rare. Using the formalism of John (1953), this paper presents a class of exact zero-gravity flows in which the free surface assumes the form of an ellipse having arbitrary but time-constant aspect ratio. The dynamically important region beneath the overturning crest of a breaking gravity wave is examined and the profile is found to be remarkably well approximated by a A √3 aspect-ratio ellipse. The range of examples presented includes high-resolution computations in both deep and shallow water, and also the plunger-generated laboratory waves of Miller (1976). The ellipse solution is shown to model qualitatively certain essential features of the numerical waves. A recent self-similar solution due to Longuet-Higgins (1981, 1982), in which the free surface is a parametric cubic curve, is also discussed. © 1983, Cambridge University Press. All rights reserved.
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  • 94
    Publication Date: 1983-05-01
    Description: We focus attention on an idealized granular material comprised of identical, smooth, imperfectly elastic, spherical particles which is flowing at such a density and is being deformed at such a rate that particles interact only through binary collisions with their neighbours. Using general forms of the probability distribution functions for the velocity of a single particle and for the likelihood of binary collisions, we derive local expressions for the balance of mass, linear momentum and fluctuation kinetic energy, and integral expressions for the stress, energy flux and energy dissipation that appear in them. We next introduce simple, physically plausible, forms for the probability densities which contain as parameters the mean density, the mean velocity and the mean specific kinetic energy of the velocity fluctuations. This allows us to carry out the integrations for the stress, energy flux and energy dissipation and to express these in terms of the mean fields. Finally, we determine the behaviour of these fields as solutions to the balance laws. As an illustration of this We consider the shear flow maintained between two parallel horizontal plates in relative motion. © 1983, Cambridge University Press. All rights reserved.
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  • 95
    Publication Date: 1983-05-01
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  • 96
    Publication Date: 1983-04-01
    Description: If different contaminant species are subject to different transverse drift rates (e.g. gravitational settling), then there is a tendency for the species to separate out. The efficiency of this separation depends upon the relative shapes of the longitudinal concentration distributions. Jayaraj & Subramanian (1978) have drawn attention to the disparity between their computed skew concentration distributions and the symmetric Gaussian distributions predicted by one-dimensional diffusion models. Here it is shown that a one-dimensional delay-diffusion model yields suitably skew predictions. The model equation is used to investigate the extent to which the separation of different contaminant species can be improved by pre-treating the sample (i.e. allowing differential drift) in a stationary fluid before being eluted into the shear flow. Pretreatment is found to be very effective for plane Poiseuille flow but not for the thermogravitational columns. © 1983, Cambridge University Press. All rights reserved.
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  • 97
    Publication Date: 1983-04-01
    Description: Nonlinear electrohydrodynamic Rayleigh-Taylor instability is investigated. A charge-free surface separating two semi-infinite dielectric fluids influenced by a normal electric field is subjected to nonlinear deformations. We use the method of multiple-scale perturbations in order to obtain uniformly valid expansions near the cutoff wavenumber separating stable from unstable flows. We obtain two nonlinear Schrodinger equations by means of which we can deduce the cutoff wavenumber and analyse the stability of the system. It is found that if a finite-amplitude wave exists then its small modulation is stable. We also obtain the surface elevation for such waves. The electric field plays a dual role in the stability criterion and the dielectric constant plays a distinctive role in this analysis. If the dielectric constant of the upper fluid is smaller than that of the lower fluid the field has a destabilizing effect for large wavenumbers. For relatively smaller wavenumbers the electric field stabilizes considerable parts of the first and second subharmonic regions in the stability diagrams; a result which is in contrast with the linear theory. If the dielectric constant of the upper fluid is larger than that of the lower fluid, then the field is stabilizing for larger values of the wavenumber K' when p is small (p is the density ratio) and destabilizing for smaller values of K'. © 1983, Cambridge University Press. All rights reserved.
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  • 98
    Publication Date: 1983-05-01
    Description: This paper describes the flow of a homogeneous fluid contained in a rapidly rotating cylinder. The upper part of the cylinder rotates slightly faster, giving rise to a discontinuity in the sidewall velocity. The Stewartson-layer structure arising at the sidewall is essentially affected by this discontinuity. In contrast with previously studied problems, the E¼ layer (E is the Ekman number) is unable to perform the matching of the interior flow to the sidewall. It is shown that this matching is carried out partially by the E¼ layer and partially by the E⅓ layer, the latter accounting for the jump discontinuity. This paper also presents an analytical description of the flow in the singularity region near the sidewall discontinuity. © 1983, Cambridge University Press. All rights reserved.
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  • 99
    Publication Date: 1983-04-01
    Description: The pattern of dispersion and uptake of an inhaled slug of tissue-soluble gas is examined within a branching model of the bronchial airways of the human lung, considered as an assembly of segments from infinitely long, straight rigid tubes with absorbing walls of finite thickness. The model is based on the first three (time-dependent) spatial moments of the solute distribution in such tubes, determined by the Aris method of moments. Poiseuille flow in each airway is assumed, and the solute distribution is taken to be initially zero in the tissue and radially uniform in the gas. First, the time dependence of axial velocity and mixing coefficient of the advancing solute in infinitely long tubes is shown and the mechanisms responsible are discussed. Transit times, uptake, uptake efficiency and mixing coefficient predicted from the model are then shown for different flow rates and solubilities, as functions of the generation of branching. As is expected, greater penetration is found for lower-solubility gases. However, of greater interest is the model prediction that uptake decreases with increasing flow rate whereas uptake efficiency increases, a result consistent with experimental indications. Finally, the mixing coefficient is shown to fall, with distance into the lung, to a value which may be much smaller than the molecular diffusivity, depending on the solubility. © 1983, Cambridge University Press. All rights reserved.
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  • 100
    Publication Date: 1983-04-01
    Description: Elementary calculations indicate that the effect of the Earth’s rotation is likely to be important in the dynamics of most internal waves in oceans, lakes and the atmosphere. Here we present measurements of the structure and properties of one class of such waves, namely solitary internal Kelvin waves, in which the Coriolis force generated by wave motion in a stratified fluid is opposed by a pressure gradient and hence change in wave amplitude along its crest. We confirm that the wave speed is independent of the rate at which the system rotates and depends only on the stratification and maximum wave amplitude. However, rotation is shown to have a large effect on both the rate at which the amplitude varies with time and the ‘cross-stream’ structure of the wave. In accordance with well-established theory, the amplitude transverse to the direction of propagation varies exponentially. This results in a decreasing wave speed with increasing distance from the wall, which in turn requires the wave front be curved backwards in order for the wave as a whole to propagate at a speed given by its maximum amplitude. Such a front curvature is not contained within the available theories. The rapid decay of wave amplitude is found to be due to the generation of inertial waves in the homogeneous fluid above and below the internal wave, and a reasonably successful scaling of this effect has been found. We also discuss the adjustment of the waves to geostropic balance and comment on applications of our results to natural systems. © 1983, Cambridge University Press. All rights reserved.
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