bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some electrically driven flows in magnetohydrodynamics Part 3. The asymptotic theory for flow between circular electrodes
Authors: Hunt J. C. R. , Stewartson K. 
Published: March 2006

In this, the third, part we present a complete asymptotic analysis of the distribution of velocity and electric potential in an electrically conducting liquid between two circular electrodes of finite diameter, 2b, when a current is passed between them. The electrodes are set opposite to each other in insulating planes, a distance 2aapart, and a magnetic field is applied perpendicular to these planes.The asymptotic solution is obtained under the restriction that the Hartmann numberMsatisfies both the conditionsM[Gt ] 1 andM½l[Gt ] 1, wherel=b/a. It enables us to calculate the distribution of velocity and electrical potential throughout the flow field, and provides an expansion for the resistanceRbetween the electrodes in descending powers ofM½l, which is correct provided terms of orderM−1and (lM½)−3are neglected. Comparison of the theoretical results with experiment shows good agreement in the measurements ofRand in the direct probe measurements of electrical potential within the fluid. This is one of the first experiments in which direct probe measurements of an MHD flow, as well as external measurements, have provided such a satisfactory confirmation of the theory. Direct measurements of the velocity, by means of a Pitot tube as in part 2, or by means of a hot-film anemometer undertaken by Malcolm (1968), agree less well with the theory.
Axisymmetric turbulent mass transfer in a circular tube
Authors: Quarmby Alan , Anand R. K. 
Published: March 2006

Solutions of the diffusion equation are obtained for mass transfer in a fully developed turbulent flow in a plain circular tube in two axisymmetric situations. The cases studied are a point source positioned at the centre of the tube and a ring source in the tube wall in which there is a uniform mass flux along a short length of the tube. The purpose of the work is to establish the correctness of the descriptions of the velocity profile and radial eddy diffusivities of mass and momentum in order to provide a firm base from which consideration of the non-axisymmetric situation could proceed.The turbulent velocity profile is deduced from a two-part model based on a sublayer profile and the Von Kármán similarity hypothesis. The radial eddy diffusivity of momentum is described by an expression due to Reichardt and Van Driest and from this the radial eddy diffusivity of mass as a function of radius is obtained by use of a ratio which takes account of fluid properties and the value of the radial eddy diffusivity.The analysis is substantiated by experiments carried out with nitrous oxide, Schmidt number = 0·77, for Reynolds numbers from 20,000 to 130,000. The concentration profiles measured at several axial positions downstream from the source are in good agreement with the analytical solutions in both cases. Direct measurements of the eddy diffusivity of mass and momentum were obtained as added confirmation and also gave good agreement with the theory.
Non-axisymmetric turbulent mass transfer in a circular tube
Authors: Quarmby Alan , Anand R. K. 
Published: March 2006

Theory and experiment are presented for mass transfer into a fully developed turbulent flow in a plain circular tube in two non-axisymmetric cases. The cases studied are a diametral line source and a discontinuous ring source, in which there is a uniform mass flux over rectangular areas of the tube wall. A comparison is made between the concentration profiles predicted by the solutions of the diffusion equation and experiments using nitrous oxide, Schmidt number S = 0·77, as a tracer gas in air. The range of experiments covers Reynolds numbers R from 20,000 to 120,000.In the analysis, the assumption is made that the tangential and radial eddy diffusivities of mass are equal at a point. The radial diffusivity of mass, which is a function of radial position, is related to the radial eddy diffusivity of momentum by a ratio, which takes account of fluid properties and the value of the radial eddy diffusivity of momentum. The satisfactory agreement between analysis and experiment establishes the correctness of this assumption. Further confirmation was obtained by direct evaluation of the tangential eddy diffusivity of mass from the measured concentration profiles.
On the non-linear Lamb-Taylor instability
Authors: Nayfeh Ali Hasan 
Published: March 2006

A non-linear analysis of the inviscid stability of the common surface of two superposed fluids is presented. One of the fluids is a liquid layer with finite thickness having one surface adjacent to a solid boundary whereas the second surface is in contact with a semi-infinite gas of negligible density. The system is accelerated by a force normal to the interface and directed from the liquid to the gas. A second-order expansion is obtained using the method of multiple time scales. It is found that standing as well as travelling disturbances with wave-numbers greater than$K^{\prime}_c = k_c[1+\frac{3}{8}a^2k^2_c + \frac{51}{512}a^4k^4_c]^{\frac{1}{2}}$where a is the disturbance amplitude and kc is the linear cut-off wave-number, oscillate and are stable. However, the frequency in the case of standing waves and the wave velocity in the case of travelling waves are amplitude dependent. Below this cut-off wave-number disturbances grow in amplitude. The cut-off wave-number is independent of the layer thickness although decreasing the layer thickness decreases the growth rate. Although standing waves can be obtained by the superposition of travelling waves in the linear case, this is not true in the non-linear case because the amplitude dependences of the wave speed and frequency are different. A mechanism is proposed to explain the overstability behaviour observed by Emmons, Chang & Watson (1960).
A visual investigation of the wall region in turbulent flow
Authors: Corino E. R. , Brodkey Robert S. 
Published: March 2006

The objective of this study is to investigate for turbulent flow the fluid motions very near a solid boundary, and to create a physical picture which relates these motions to turbulence generation and transport processes. An experimental technique was developed which permitted detailed observations of the regions very near a pipe wall, including the viscous sublayer, without requiring the introduction of any injection or measuring device into the flow. This technique involved suspending solid particles of colloidal size in a liquid, and photographing their motions with a high-speed motion picture camera moving with the flow. To provide greater detail, the field of view was magnified.Fluid motions were observed to change in character with distance from the wall. The sublayer was continuously disturbed by small-scale velocity fluctuations of low magnitude and periodically disturbed by fluid elements which penetrated into the region from positions further removed from the wall. From a thin region adjacent to the sublayer, fluid elements were periodically ejected outward toward the centreline. Often there was associated with these events a zone of high shear at the interface between the mean flow and the decelerated region that gave rise to the ejected element. When the ejected element entered this shear zone, it interacted with the mean flow and created intense, chaotic velocity fluctuations. These ejections and resulting fluctuations were the most important feature of the wall region, and are believed to be a factor in the generation and maintenance of turbulence.
Turbulent boundary-layer flow on a rotating disk
Authors: Cham T-S. , Head M. R. 
Published: March 2006

Calculations have been made of the development of the turbulent boundary layer on a disk rotating in free air, using circumferential and radial momentum-integral equations and an auxiliary equation of entrainment. In the calculations, circumferential velocity profiles are represented by Thompson's (1965) two-parameter family, while radial profiles are given by Mager's (1952) quadratic expression. The circumferential component of skin friction follows from the use of Thompson's profile family for the circumferential velocity. The entrainment, in dimensionless form, is assumed to be determined uniquely by the circumferential velocity profile in the same way as was proposed by Head (1958) for a two-dimensional turbulent boundary layer.Detailed measurements have been made of the development of the turbulent boundary layer on the rotating disk, and the calculations are found to be in excellent agreement with the results when a suitable adjustment is made to Head's two-dimensional entrainment curve.
Slow oscillations in an ocean of varying depth Part 1. Abrupt topography
Authors: Rhines P. B. 
Published: March 2006

This paper is part of a study of quasigeostrophic waves, which depend on the topography of the ocean floor and the curvature of the earth.In a homogeneous, β-plane ocean, motion of the fluid across contours of constantf/hreleases relative vorticity (fis the Coriolis parameter andhthe depth). This well-known effect provides a restoring tendency for either Rossby waves (withhconstant) or topographic waves over a slope. The long waves in general obey an elliptic partial differential equation in two space variables. Because the equation has been integrated in the vertical direction, the exact inviscid bottom boundary condition appears in variable coefficients.When the depth varies in only one direction the equation is separable at the lowest order in ω, the frequency uponf. With a simple slope, |[xdtri ]h/h| = constant, the transition from Rossby to topographic waves occurs at |[xdtri ]h| ∼h/Re, where Reis the radius of the earth. Isolated topographic features are considered in §2. It is found that a step of fractional height δ on an otherwise flat ocean floor reflects the majority of incident Rossby waves when δ > 2ω. In the ocean ω is usually small, due to continental barriers, so even slight depth variations are important. A narrowridgedoes not act as a great obstruction but calculations show, for example, that the Mid-Atlantic Ridge is broad enough to reflect all but the lowest mode Rossby waves in the North Atlantic.Besides isolating oceanic plains from one another, steps and ridges support trapped topographic waves of greatest frequency ∼ δ/2, analogous to the potential well solutions in quantum mechanics. These waves cannot carry energy alongabrupttopography, but they disperse more rapidly over broader slopes; the phase and group speeds may be hundreds of cm/sec. The continentalshelf waves found by Robinson are an example of the latter case. There are many such wave guides, where thef/hcontours are crowded, in the deep ocean.The theory suggests that measurement of Rossby waves will rarely be possible at the coast of a continent.
Slow oscillations in an ocean of varying depth Part 2. Islands and seamounts
Authors: Rhines P. B. 
Published: March 2006

We consider slow oscillations trapped about axisymmetric islands and seamounts. ω is in the range [lsim ] δ/2 (ω is the frequency divided by f, the Coriolis parameter, and δ the fractional change in depth). The periods, for example, are [gsim ] 2·4 days for an island with a sloping ‘skirt’, h [vprop ] r½, where h is the depth and (r, θ) are polar co-ordinates in the plane tangent to the mean sea surface. Energy leaks slowly away from the topography in Rossby waves. In the limiting case of a cylindrical island with vertical walls there are no such trapped motions, but incident Rossby waves are scattered anisotropically. If γ, the ratio of the island radius, a, to the Rossby wavelength, is small, the scattering cross-section ∼ γ3a. The free oscillations at seamounts and islands with skirts allow much stronger scattering (with cross-section ∼ a/γ, ∼ a wavelength), when one of their frequencies is near that of the incident wave.The theory suggests that measurements of Rossby waves will be possible at small islands, but that the many local oscillations in the same frequency range will add some confusion.
On the reflexion of wave characteristics from rough surfaces
Authors: Longuet-Higgins M. S. 
Published: March 2006

The energy of internal waves tends to be propagated along certain characteristic paths inclined at fixed angles to the vertical direction; the angle of inclination depending only on the wave frequency and the density stratification (not on the wavelength). The reflexion of such waves by smooth plane surfaces has been discussed recently by Sandstrom (1966).In the present paper the role of surface roughness is examined. Surprisingly, it appears that quite small-scale irregularities can completely alter the reflecting properties of a surface; the tangential scale of the roughness elements may be much smaller than the wavelength of the incident or reflected waves. All scales of roughness are relevant, down to those comparable in magnitude to the thickness of the oscillatory boundary layer. For tidal waves in the ocean this thickness is of the order of 1 m.The behaviour of the coefficient of transmission as a function of the angle of incidence appears at first sight to be extremely complicated. Some simple examples of periodic surface roughnesses are discussed and elucidated: a sawtooth, a square-topped wave and a simple sine-wave. The transmission coefficientTfor a sine-wave, for example, is shown in figure 9. An approximate expression forTis also derived in the case of a slowly modulated sine-wave (figure 10). These results are for a non-viscous fluid. The effects of viscosity are also considered qualitatively.
Effects of sound on separated flows
Authors: Peterka Jon A. , Richardson Peter D. 
Published: March 2006

Measurements of flow and fluctuating heat transfer were made for a circular cylinder in cross-flow with a transverse standing sound field imposed simultaneously. Reynolds numbers were of the order of 104, known to be in the disturbance-sensitive range, and sound intensities were as large as 140 db. The frequencies of the sound field were of the order of the disturbance frequency in the separated shear layers, reported first by Bloor.With a sound field having its frequency matched sufficiently closely to that occurring naturally in the shear layer, the growth of the instability is enhanced with the processes of vortex fusion and possibly vortex breakdown being detectable. At the same time, the vortex street frequency is only very weakly affected, although the vortex formation region length is reduced when the instability in the shear layer is enhanced. It is suggested that the discretization of vorticity in the shear layers is one factor significant in reducing the formation length. Heat transfer at the rear of the cylinder fluctuates at frequencies centred on the shedding frequency. The fluctuation level increases as the formation region shortens.
Smoke observations of the formation of a Kármán vortex street
Authors: Zdravkovich M. M. 
Published: March 2006

A smoke visualization technique was used to study the laminar wake behind a single cylinder. Observations of the wake revealed the nature of the process of formation of a Kármán vortex street: instability of the shear layers was coupled with the rolling up process induced by the concentration of vorticity.An unexpected mass transfer was observed through the Kármán vortex street which cause mixing of the fluid surrounding the wake.
The calculation of three-dimensional turbulent boundary layers in incompressible flow
Authors: Nash J. F. 
Published: March 2006

A method is described for calculating the development of a three-dimensional turbulent boundary layer, over a flat or developable surface, in incompressible flow. The method involves the numerical integration of the equations of motion by an explicit finite-difference method. The shear stress is determined by a parallel integration of the turbulent energy equation modified by the inclusion of empirical functions of a form which has proved successful in two dimensions, and the additional assumption is made that the turbulent shear stress acts in the direction of the rate of strain of the mean motion. The treatment of the turbulent energy equation follows closely the work of Bradshaw, Ferriss & Atwell (1967) in two dimensions.Comparison with experiment is found to be substantially more difficult than in two dimensions. Particular difficulty is encountered in translating the recorded details of the experiment into boundary conditions for the calculation. The comparisons submitted here give some indication that the method as a whole performs satisfactorily, but they do not provide a definitive assessment of the validity of the basic assumptions. A plea is made for an experiment to supply data in a suitable form for making a more careful assessment of methods of this type.
Numerical integration of the three-dimensional Navier-Stokes equations for incompressible flow
Authors: Williams Gareth P. 
Published: March 2006

A method of numerically integrating the Navier-Stokes equations for certain three-dimensional incompressible flows is described. The technique is presented through application to the particular problem of describing thermal convection in a rotating annulus. The equations, in cylindrical polar co-ordinate form, are integrated with respect to time by a marching process, together with the solving of a Poisson equation for the pressure. A suitable form of the finite difference equations gives a computationally-stable long-term integration with reasonably faithful representation of the spatial and temporal characteristics of the flow.Trigonometric interpolation techniques provide accurate (discretely exact) solutions to the Poisson equation. By using an auxiliary algorithm for rapid evaluation of trigonometric transforms, the proportion of computation needed to solve the Poisson equation can be reduced to less than 25% of the total time needed to’ advance one time step. Computing on a UNIVAC 1108 machine, the flow can be advanced one time-step in 2 sec for a 14 × 14 × 14 grid upward to 96 sec for a 60 × 34 × 34 grid.As an example of the method, some features of a solution for steady wave flow in annulus convection are presented. The resemblance of this flow to the classical Eady wave is noted.
Peristaltic pumping with long wavelengths at low Reynolds number
Authors: Shapiro A. H. , Jaffrin M. Y. , Weinberg S. L. 
Published: March 2006

Pumping by means of an infinite train of peristaltic waves is investigated under conditions for which the relevant Reynolds number is small enough for inertial effects to be negligible and the wavelength to diameter ratio is large enough for the pressure to be considered uniform over the cross-section. Theoretical results are presented for both plane and axisymmetric geometries, and for amplitude ratios ranging from zero to full occlusion. For a given amplitude ratio, the theoretical pressure rise per wavelength decreases linearly with increasing time-mean flow. An experiment with a quasi-two-dimensional apparatus confirmed the theoretical values.Calculations of the detailed fluid motions reveal that under many conditions of operation the net time-mean flow is the algebraic difference between a forward time-mean flow in the core of the tube and a backward (‘reflux’) time-mean flow near the periphery. The percentage of reflux flow can be very high. This reflux phenomenon is probably of physiologic significance in the functioning of the ureter and the gastro-intestinal system. A second fluid-mechanical peculiarity with physiological implications is that of ‘trapping’: under certain conditions an internally circulating bolus of fluid, lying about the axis, is transported with the wave speed as though it were trapped by the wave.
Boundary-value problems in the kinetic theory of gases Part I. Slip flow
Authors: Williams M. M. R. 
Published: March 2006

A new method for treating boundary-value problems in gas-kinetic theory has been developed. The new method has the advantage of reproducing the bulk or asymptotic flow properties accurately whilst giving a realistic description of the behaviour of the molecular distribution function in the neighbourhood of a wall. As an example, the Kramers, or slip-flow, problem is solved for a general specular-diffuse boundary condition and some new expressions for the slip coefficient, flow speed and molecular distribution function at the surface are derived.A brief discussion of the eigenvalue spectrum of the associated Boltzmann equation is given and its physical significance pointed out.Certain analogies between this problem and the Milne problem in neutron transport theory are demonstrated.
Hydromagnetic stability of dissipative flow between rotating permeable cylinders. Part 2. Oscillatory critical modes and asymptotic results
Authors: Chang Tien Sun , Sartory Walter K. 
Published: March 2006

In considering the onset of instability of an electrically conducting fluid between rotating permeable perfectly conducting cylinders in an applied axial magnetic field, it is found that oscillatory axially symmetric modes occur at large values of Hartmann number, in addition to the usual stationary modes. Results are presented showing the effect of the oscillatory modes on the criterion of onset of instability.The asymptotic behaviour of the stability criterion is considered in the limit of very large radial Reynolds number, and also in the limit where both the radial Reynolds number and the Hartmann number are large.
Buoyancy-driven convection in cylindrical geometries
Authors: Liang S. F. , Vidal A. , Acrivos Andreas 
Published: March 2006

Numerical solutions to the Boussinesq equations containing a temperature-dependent viscosity are presented for the case of axisymmetric buoyancy-driven convective flow in a cylindrical cell. Two solutions, one with upflow and the other with downflow at the centre of the cell, were found for each set of boundary conditions that were considered. The existence of these two steady-state régimes was verified experimentally for the case of a cylindrical cell having rigid insulating lateral boundaries and isothermal top and bottom planes.Using a perturbation expansion it is also shown that only one of these solutions remains stable in the subcritical régime. This, however, seems to be confined to a very narrow range of Rayleigh numbers, beyond which, according to all the evidence presently at hand, both solutions are equally stable for those values of the Rayleigh and Prandtl numbers for which axisymmetric motions occur.Finally, certain fundamental differences between the problem considered here and that of thermal convection in a layer of infinite horizontal extent are briefly discussed.