bluuebunny/crossref_metadata_2025 huggingface dataset:
A three-dimensional solution for waves in the lee of mountains
Authors: Crapper G. D.
Published: March 2006

This paper presents a three-dimensional small-perturbation approach to the problem of waves produced in a statically stable stratified air stream flowing over a mountain. The fundamental solution for a doublet disturbance in an air stream in which the parameter l2 = gβ/V2 is constant is calculated, and then is extended to that for a disturbance due to a circular mountain in the same air stream. A simple approximation to the known two-dimensional flow over an infinite ridge is also given. The second (’upper’) boundary condition for the solutions is determined in a rigorous analytical manner, assuming the presence of small friction forces, or, alternatively, of time dependence. It is hoped that this will settle the controversy which exists over the choice of this condition.

The results show that the behaviour due to a doublet is peculiar and not truly representative of that due to a mountain. The latter shows waves which decay down-stream and are contained in a strip, the width of the strip being determined by the radius of the mountain. An interesting result is that the circular mountain can give rise to waves which have greater amplitude than those produced by the infinite ridge under the same conditions.

In some previous papers the waves produced by the infinite ridge have been neglected, but the present paper shows that in many cases this procedure is not justifiable. The detailed solution for the waves behind a circular mountain has a form which emphasizes the importance for lee-wave production of ’resonance’ between the width of the mountain and the characteristic length l-1 of the air stream.
The rise of a gas bubble in a viscous liquid
Authors: Moore D. W.
Published: March 2006

The rise of a gas bubble in a viscous liquid at high Reynolds number is investigated, it being shown that in this case the irrotational solution for the flow past the bubble gives a uniform approximation to the velocity field. The drag force experienced by the bubble is calculated on this hypothesis and the drag coefficent is found to be 32/R, where R is the Reynolds number (based on diameter) of the bubbles rising motion. This result is shown to be in fair agreement with experiment.

The theory is extended to non-spherical bubbles and the relation of the resulting theory, which enables both bubble shape and velocity of rise to be predicted, to experiment is discussed.

Finally, an inviscid model of the spherical cap bubble involving separated flow is considered.
On the instability theory of the melted surface of an ablating body when entering the atmosphere
Authors: Feldman Saul
Published: March 2006

Some ablating bodies entering the atmosphere will melt or soften. Under deceleration, the soft or melted surface will tend to develop instabilities of the Lamb-Taylor type. Two situations involving viscous incompressible fluids are investigated here: one where the liquid layer has constant viscosity and finite thickness, and the other, where the viscosity increases exponentially with distance away from the interface, and the layer is semi-infinite in extent.

It can be demonstrated, that if one neglects gradients in the flow direction, the rate of growth of interface disturbances in a plane normal to the axis of an axially symmetric blunt body is independent of the flow velocity. The fact that the deceleration and liquid thickness vary with time along a trajectory is also included in the analysis. Results of calculations for the amplification factor and the most amplified wavelength are given.

A mechanism due to the deceleration is postulated, which would cause the formation of longitudinal grooves on the surface of an axially symmetric blunt body while entering the atmosphere.
Shearing flow over a wavy boundary
Authors: Benjamin T. Brooke
Published: March 2006

A theoretical study is made of shearing flows bounded by a simple-harmonic wavy surface, the main object being to calculate the normal and tangential stresses on the boundary. The type of flow considered is approximately parallel in the absence of the waves, being exemplified by two-dimensional boundary layers over a plane. Account is taken of viscosity; but, as the Reynolds number is assumed to be large, its effects are seen to be confined within narrow ‘friction layers’, one of which adjoins the wave and another surrounds the ‘critical point’ where the velocity of flow equals the wave velocity. The boundary conditions are made as general as possible by including the three cases where respectively the boundary is rigid, flexible yet still solid, or completely mobile as if it were the interface with a second fluid.

The theory is developed on the model of stable laminar flow, although it is proposed that the same theory may usefully be applied also to examples of turbulent flow considered as ‘pseudo-laminar’ with velocity profiles corresponding to the mean-velocity distribution. Use is made of curvilinear co-ordinates which follow the contour of the wave-train. This admits a linearized form of the problem whose validity requires only that the wave amplitude be small in comparison with the wavelength, even when large velocity gradients exist close to the boundary. The analysis is made largely without restriction to particular forms of the velocity profile; but eventually consideration is given to the example of a linear profile and the example of a boundary-layer profile approximated by a quarter-period sinusoid. In § 7 some general methods are set out for the treatment of disturbed boundary-layer proses: these apply with greatest precision to thin boundary layers, but are also useful for the initially very steep but on the whole fairly diffuse profiles which occur in most practical instances of turbulent flow over waves.

The phase relationships found between the stresses and the wave elevation are discussed for several examples, and their interest in connexion with problems of wave generation by wind is pointed out. It is shown that in most circumstances the stresses are distributed in much the same way as if the leeward slopes of the waves were sheltered. For instance, the pressure distribution often has a substantial component in phase with the wave slope, just as if a wake were formed behind each wave crest—although of course actual separation effects are outside the scope of the present theory. In this aspect, the analysis amplifies the work of Miles (1957).
Reverse flow and supersonic interference
Authors: Clarke Joseph H.
Published: March 2006

First, from a volumetric formulation of the momentum theorem of linearized theory, a general analytic proof is presented of the invariance of the drag of an arbitrary spatial distribution of horseshoe vortices and sources under reversal of the undisturbed flow. By consideration of the interference drag of two such singularity distributions, a reverse-flow relation for steady subsonic or supersonic flow is then obtained. This relation, a generalization of the Ursell-Ward theorem, may be applied to configurations with bodies whose surfaces are not quasi-cylindrical and whose surface pressures are quadratically related to the perturbation velocity.

The relation is used to discuss several interfering two-body arrangements in supersonic flow. It is shown that, in certain cases, the drag and lift may be determined without knowledge of the interference flow field associated with the arbitrarily prescribed body geometry. The simplicity of the results permits the formulation of optimum problems. The invariance of the drag under flow reversal with unchanged geometry is also established.
On the stability of a shear layer
Authors: Menkes J.
Published: March 2006

The effects of density variation in the absence of gravity on the stability of a horizontal shear layer between two streams of uniform velocities is investigated. The density is assumed to decrease exponentially with height and the velocity is represented by U(y) = tanh y.

The method of small disturbances is employed to obtain the neutral stability curve. It is demonstrated that disturbances with wave-numbers larger than the width of the transition layer are attenuated.

Qualitative agreement with experimental evidence is obtained.
Pressure drop due to viscous flow through cylinders
Authors: Brenner Howard
Published: March 2006

A general formula is developed which permits a calculation of the pressure drop arising from the slow steady flow of a viscous fluid through a circular cylinder for arbitrarily assigned conditions of velocity on the bounding surfaces of the cylinder. In particular, the diminution in pressure can be calculated directly from the prescribed boundary velocities without requiring a detailed solution of the equations of motion. Hence it is possible to compute, in comparatively simple fashion, the magnitude of this macroscopic parameter for a large variety of complex motions which would normally present great analytical difficulties.

By way of illustration the additional pressure drop arising from the presence of a point force situated along the axis of a cylinder is calculated. The additional force required to maintain the motion in the presence of the obstacle is exactly twice the magnitude of the point force itself.
Experiments on the flow past a circular cylinder at low Reynolds numbers
Authors: Tritton D. J.
Published: March 2006

Part I describes measurements of the drag on circular cylinders, made by observing the bending of quartz fibres, in a stream with the Reynolds number range 0·5-100. Comparisons are made with other experimental values (which cover only the upper part of this range) and with the various theoretical calculations.

Part II advances experimental evidence for there being a transition in the mode of the vortex street in the wake of a cylinder at a Reynolds number around 90. Investigations of the nature of this transition and the differences between the flows on either side of it are described. The interpretation that the change is between a vortex street originating in the wake and one originating in the immediate vicinity of the cylinder is suggested.
Steady finite motions of a conducting liquid
Authors: Long Robert R.
Published: March 2006

In certain cases of steady motion of a conducting fluid in a magnetic field, the primitive equations may be integrated once, yielding a second-order partial differential equation in the stream function. This equation is highly non-linear in general, but for certain choices of basic flow and magnetic fields it is tractable. Several arbitrary functions of integration have to be evaluated to make the analysis useful. This may be done in a region that remains undisturbed. A short discussion is given to suggest a procedure for deciding in a special case whether this undisturbed region is ‘upstream’ or ‘downstream’.
Inviscid flow of a reacting mixture of gases around a blunt body
Authors: Lick Wilbert
Published: March 2006

A general numerical procedure is described whereby the details of the steady inviscid flow of a mixture of perfect gases about a blunt body, including the effects of finite dissociation and recombination rates, may be calculated. Several numerical examples are calculated in order to apply the numerical procedure to specific cases and also to show the effects of finite reaction times on the flow about a blunt body.
Temperature fluctuations in the atmospheric boundary layer
Authors: Priestley C. H. B.
Published: March 2006

A systematic analysis is made of published measurements of the magnitude of temperature fluctuations in the atmospheric boundary layer. These cover a wide range of height, wind speed, and thermal stratification. Within appropriate ranges of the variables, there is evidence for the existence of a dominantly forced convection régime, and also one wherein the predictions of the similarity theory of free convection are fairly closely approached. Subject to the limitations set by the recording systems used, regression relations are obtained for the magnitude of the fluctuations in terms of height and vertical temperature gradient or heat flux.
An experiment on the stability of hypersonic laminar boundary layers
Authors: Demetriades Anthony
Published: March 2006

An experimental investigation of the hydrodynamic stability of the laminar hypersonic boundary layer was carried out with the aid of a hot-wire anemometer. The case investigated was that of a flat surface at zero angle of attack and no heat transfer.

The streamwise amplitude variation of both natural disturbances and of disturbances artifically excited with a siren mechanism was studied. In both cases it was found that such small fluctuations amplify for certain ranges of frequency and Reynolds numberRθ, and damp for others. The demarcation boundaries for the amplification (instability) zone were found to resemble the corresponding limits of boundary-layer instability at lower speeds. A ‘line of maximum amplification’ of disturbances was also found. The amplification rates and hence the degree of selectivity of the hypersonic layer were found, however, to be considerably lower than those at the lower speeds. The disturbances selected by the layer for maximum amplifications have a wavelength which was estimated to be about twenty times the boundary-layer thickness δ.
A comparison between buoyant vortex rings and vortex pairs
Authors: Turner J. S.
Published: March 2006

In this paper it is shown how earlier results for buoyant vortex rings may be extended to describe the corresponding two-dimensional case, which arises in the theory of bent-over plumes. It is again assumed that in uniform surroundings the circulation remains constant while the buoyancy acts to increase the momentum of the pair. The behaviour in two dimensions is quite different from that in three, however; a buoyant vortex ring spreads linearly with height, whereas a buoyant pair spreads exponentially with height, or linearly with time (and therefore, in a bent-over plume, linearly with distance downwind).

The theory has been extended to describe the rise of buoyant rings and pairs through stably stratified surroundings having a linear density gradient. The behaviour near the maximum height reached is found to depend critically in both cases on the relative rates at which the circulation and the momentum fall to zero. If these reach zero together, the rings or pairs will steadily increase in size and come to rest at a finite height and with a finite radius. If the circulation is non-zero when the momentum vanishes, the radius begins to decrease soon after the buoyancy becomes zero, and the vortices will therefore tend to break up suddenly and mix into their surroundings. There is a considerable increase in the final height which should be attained by vortex rings or bentover plumes if the initial circulation is increased; it is suggested that releasing smoke intermittently, rather than continuously, at high velocity might be a means of increasing the effective height of chimneys in calm conditions. When the circulation reaches zero before the momentum does, the solutions indicate that the radius becomes very large near the level of zero buoyancy.
The stability of free boundary layers between two uniform streams
Authors: Tatsumi T. , Gotoh K.
Published: March 2006

Hydrodynamic stability of free boundary-layer flows is treated in general. It is found that the situations at low Reynolds numbers are universal for all velocity profiles of free boundary-layer type. Curves of constant amplification are calculated as far as O(R3). In particular, the asymptotic form of the neutral curves for R [eDot ] 0 is found to be α = R/(4√3), so that the critical Reynolds numbers of these flows are identically zero. The phase velocity of the disturbance is also found to be zero, for all disturbances, up to the second approximation.

A method of normalizing the velocity profiles is suggested, and existing results for the stability of various profiles at large Reynolds numbers are discussed from a new point of view.
On the generation of surface waves by turbulent shear flows
Authors: Miles John W.
Published: March 2006

The model proposed by Phillips (1957) for the generation of water waves by the random fluctluations of normal pressure already present in a turbulent wind is generalized to include energy transfer associated with the interaction between surface wave and mean air flow (Miles 1957). It is found that this energy transfer may increase by an order of magnitude the surface displacements produced by a given distribution of pressure fluctuations in the principal stage of development.
On the flow of a conducting fluid past a magnetized sphere
Authors: Ludford G. S. S. , Murray J. D.
Published: March 2006

In the steady flow of an incompressible, inviscid, conducting fluid past a magnetized sphere, the first-order effects of the magnetic field and the conductivity are studied. Paraboloidal wakes of vorticity and magnetic intensity are formed, the former being half the size of the latter. The vorticity, generated by the non-conservative electromagnetic force, is logarithmically infinite on the sphere. For the case of a dipole of moment M at the centre of a sphere of radius a, the drag coefficient is
$C_D = \frac {144 \mu^{\prime 2}}{5(2\mu + \mu^{\prime})^2} \beta R_M,$
where μ and μ′ are the permeabilities of the fluid and sphere, respectively, β is the ratio of the representative magnetic pressure μM2/2a6 to the free-stream dynamic pressure, and RM is the magnetic Reynolds number.
The Stokes flow problem for a class of axially symmetric bodies
Authors: Payne L. E. , Pell W. H.
Published: March 2006

The Stokes flow problem is concerned with fluid motion about an obstacle when the motion is such that inertial effects can be neglected. This problem is considered here for the case in which the obstacle (or configuration of obstacles) has an axis of symmetry, and the flow at distant points is uniform and parallel to this axis. The differential equation for the stream function ψ then assumes the form L2−1ψ = 0, where L−1 is the operator which occurs in axiallysymmetric flows of the incompressible ideal fluid. This is a particular case of the fundamental operator of A. Weinstein's generalized axially symmetric potential theory. Using the results of this theory and theorems regarding representations of the solutions of repeated operator equations, the authors (1) give a general expression for the drag of an axially symmetric configuration in Stokes flow, and (2) indicate a procedure for the determination of the stream function. The stream function is found for the particular case of the lens-shaped body.

Explicit calculation of the drag is difficult for the general lens, without recourse to numerical procedures, but is relatively easy in the case of the hemispherical cup. As examples illustrative of their procedures, the authors briefly consider three Stokes flow problems whose solutions have been given previously.
A laminar planetary jet
Authors: Long Robert R.
Published: March 2006

A theory of a jet in a rotating, viscous fluid is developed. It is suggested that it may be related to a jet observed in an experiment with a rotating spherical shell of liquid and, in addition, may partly explain the existence of the subsurface equatorial current in the Pacific Ocean. The fundamental physical idea is that of a balance of vorticity brought into the jet by advection and diffused by friction. The necessary approximations are borrowed from boundary-layer theory. The linear case is solved completely and inferences about the non-linear jet are obtained by dimensional reasoning.
The forces on wing-fuselage combinations in supersonic flow
Authors: Clarke Joseph H.
Published: March 2006

Reverse-flow relations are used to provide convenient expressions for the aerodynamic forces which act on a general wing-fuselage combination in supersonic flow. The drag, lift, spanwise and chordwise lift distributions, and wing moments are treated. Consideration is given to available methods and results, including tables, which apply to the wing-fuselage interference problem, and reverse-flow relations are then employed to effect desirable changes in the detining force expressions by introducing wings or fuselages in the reverse flow. It is shown that the aerodynamic forces can be determined from a solution for the pressure on only the fuselage surface within the domain of dependence of the wing, this region being selected on the basis of relative ease of computation. In some cases the simplification achieved is quite substantial. Certain results in the literature arise naturally as special cases. The reverse-flow theorem is re-examined in the light of the procedure considered, and it is found to be inapplicable in one respect. The difficulty is circumvented by constructing an acceptable configuration which is equipollent to the prescribed one. It appears that the method given is applicable in other linear hyperbolic problems in mathematical physics when bulk or gross information is required and a suitable reciprocity relation can be constructed.
Multiple shock compression using a piston of finite weight
Authors: Winter D. F. T.
Published: March 2006

This paper describes a theory for a piston-operated compressor in which shock waves are used to heat the gas being compressed. Detailed calculations are given showing the use of such a compressor to heat air for use in a hypersonic wind tunnel. The effect of real gas properties on the compression process is included in this discussion.
Exact solutions for steady two-dimensional flow of a stratified fluid
Authors: Yih Chia-Shun
Published: March 2006

Three classes of exact solutions for steady two-dimensional flows of a stratified fluid are found. The flows which correspond to these solutions have arbitrary amplitude (however defined). Two of the three classes of solutions have close bearings on the lee-wave problem in meteorology. It is also shown that the amplitudes of the lee-wave components (if there is more than one component) depend not on the details of the shape of the barrier, but only on certain simple integral properties of the function for the singularity distribution generating the barrier.
On the dynamics of unsteady gravity waves of finite amplitude Part 1. The elementary interactions
Authors: Phillips O. M.
Published: March 2006

This paper is concerned with the non-linear interactions between pairs of intersecting gravity wave trains of arbitrary wavelength and direction on the surface of water whose depth is large compared with any of the wavelengths involved. An equation is set up to describe the time history of the Fourier components of the surface displacement in which are retained terms whose magnitude is of order (slope)2 relative to the linear (first-order) terms. The second-order terms give rise to Fourier components with wave-numbers and frequencies formed by the sums and differences of those of the primary components, and the amplitudes of these secondary components is always bounded in time and small in magnitude. The phase velocity of the secondary components is always different from the phase velocity of a free infinitesimal wave of the same wave-number. However, the third-order terms can give rise to tertiary components whose phase velocity is equal to the phase velocity of a free infinitesimal wave of the same wave-number, and when this condition is satisfied the amplitude of the tertiary component grows linearly with time in a resonant manner, and there is a continuing flux of potential energy from one wave-number to another. The time scale of the growth of the tertiary component is of order of the (−2)-power of the geometric mean of the primary wave slopes times the period of the tertiary wave. The Stokes permanent wave appears as a special case, in which the tertiary wave-number is the same as that of the primary, but its phase is advanced by ½π. The energy transfer to the tertiary component in this case is usually interpreted as an increase in the phase velocity of the wave.

The dynamical interactions in water of finite depth are considered briefly, and it is shown that the amplitude of the secondary components becomes large (though bounded in time) as the water depth becomes smaller than the wave-length of the longest primary wave.
On two-dimensional inertial flow in a rotating stratified fluid
Authors: Robinson A. R.
Published: March 2006

An inviscid fluid is bounded above by a horizontal plane and below by finite-amplitude ridges. The fluid is rotating and stratified. A uniform transport is forced across the ridges at small dynamical Rossby number, although the boundary conditions are such that motion cannot remain geostrophic. The most significant parameter is found to be a thermal Rossby number based upon the vertical density difference and both vertical and horizontal length scales, but independent of the transport. Conditions determining whether or not effects of the bottom topography will penetrate vertically throughout the fluid are discussed. Some numbers characteristic of flow in the deep ocean are presented.
The electrical conductivity of shock-ionized argon
Authors: Pain H. J. , Smy P. R.
Published: March 2006

The electrical conductivity of shock-ionized argon has been measured at temperatures between 6000 °K and 13,000 °K and electron number densities in the range 1016 to 1018 cm−3. The results are compared with theoretically computed values and show sufficient agreement to be plotted on a linear scale. The experimental technique is based on the measurement of voltages generated in a search coil by the flux from currents induced in a plasma moving rapidly through a magnetic field.
The second approximation to cnoidal and solitary waves
Authors: Laitone E. V.
Published: March 2006

The expansion method introduced by Friedrichs (1948) for the systematic development of shallow-water theory for water waves of large wavelength was used by Keller (1948) to obtain the first approximation for the finite-amplitude solitary wave of Boussinesq (1872) and Rayleigh (1876), as well as for periodic waves of permanent type, corresponding to the cnoidal waves of Korteweg & de Vries (1895).

The present investigation extends Friedrich's method so as to include terms up to the fourth order from shallow-water theory for a flat horizontal bottom, and thereby obtains the complete second approximations to both cnoidal and solitary waves. These second approximations show that, unlike the first approximation, the vertical motions cannot be considered as negligible, and that the pressure variation is no longer hydrostatic.
Note on waves through gases at pressures small compared with the magnetic pressure, with applications to upper-atmosphere aerodynamics
Authors: Lighthill M. J.
Published: March 2006

Most treatments of magnetohydrodynamics waves have confined physical interpretation to cases when the Alfvén velocity a1 is small compared with the sound velocity a0. Here we consider the ‘low-beta situation’, in which a1, the only possible waves are longitudinal ones, propagated unidirectionally along lines of magnetic force with velocity a0. These can be interpreted as sound waves, confined to effectively rigid magnetic tubes of force. Hall-current effects do not alter these conclusions (in contrast to the high-beta situation), and finite conductivity introduces only small dissipation.

An application is made to the flow pattern around a body moving through the F2 layer of the ionosphere, where, although neutral particles have a very large mean free path, charged particles interact electrostatically and, it is argued, may be regarded as forming a continuous fluid whose movement is independent of that of the neutral particles. A body moving at satellite speed or below would then excite the above-mentioned unidirectional sound waves, but no waves at much faster Alfvén velocity. These considerations suggest that its movement would be accompanied by a [xvee ]-shaped pattern of electron density (figure 2), which might be in part responsible for some anomalous radar echoes that have been reported.
Finite tidal waves propagated without change of shape
Authors: Ball F. K.
Published: March 2006

Coriolis terms are introduced into the equations governing the motion of a finite tidal wave. Various types of solution are found, all of which travel without change of shape and some which are periodic with sharp crests and broad troughs. The classical result that such waves cannot be propagated without change of shape is therefore untrue in these circumstances.
Kinematic formulation of rotational gas flow
Authors: Vinokur M.
Published: March 2006

It is shown that for the steady isoenergetic rotational flow of an ideal gas, both the specific enthalpy and the speed of sound can be expressed as functions of the velocity. As a result, it is possible to formulate the equations of motion so that the velocity is the only dependent variable. For a gas whose enthalpy and sound speed are functionally related, the results are a generalization of those for a perfect gas. If the enthalpy and sound speed are independent variables, the new formulation leads to a single vector equation whose solution completely determines the flow.
Stability of a conducting rotating fluid of variable density
Authors: Talwar S. P.
Published: March 2006

The Rayleigh instability of an incompressible, infinitely conducting, inviscid fluid of variable density is investigated under the influence of an horizontal magnetic field and coriolis forces. After establishing the equations of the problem when both the density and the magnetic field vary with distance in the upward direction, two special cases of density distribution are studied in detail. Both the magnetic field and coriolis forces are found to have a stabilizing influence on the configuration and further it is concluded that they may bring about stability in the configuration when it is thoroughly unstable without them.
An example of steady laminar flow at large Reynolds number
Authors: Proudman Iam
Published: March 2006

The purpose of this note is to describe a particular class of steady fluid flows, for which the techniques of classical hydrodynamics and boundary-layer theory determine uniquely the asymptotic flow for large Reynolds number for each of a continuously varied set of boundary conditions. The flows involve viscous layers in the interior of the flow domain, as well as boundary layers, and the investigation is unusual in that the position and structure of all the viscous layers are determined uniquely. The note is intended to be an illustration of the principles that lead to this determination, not a source of information of practical value.

The flows take place in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. When fluid is extracted through both walls there are boundary layers on both walls and the flow outside these layers is irrotational. When fluid is extracted through one wall and injected through the other, there is a boundary layer only on the former wall and the inviscid rotational flow outside this layer satisfies the no-slip condition on the other wall. When fluid is injected through both walls there are no boundary layers, but there is a viscous layer in the interior of the channel, across which the second derivative of the tangential velocity is discontinous, and the position of this layer is determined by the requirement that the inviscid rotational flows on either side of it must satisfy the no-slip conditions on the walls.
On a circular cylinder in a steady wind at transition Reynolds numbers
Authors: Humphreys John S.
Published: March 2006

Some results of an experimental investigation of forces associated with the subsonic flow of air around a circular cylinder in a wind tunnel are presented. The oscillating forces due to the downstream vortex street are studied for Reynolds numbers in the ‘critical’ range 4 × 104 to 6 × 105. Of particular interest is the observation, at the onset of transition to turbulence, of a spanwise wave or cell pattern near the cylinder surface, which is stabilized in a striking manner by the use of the fine threads as a visualization technique.
The viscosity of a suspension of spheres
Authors: Maude A. D.
Published: March 2006

It is shown that in Stokes's flow the perturbation field, due to the addition of one more sphere to a shear flow of a fluid containing a number of non-interacting spheres, has the property that the total additional shearing force, acting on any plane normal to the direction of velocity change, is zero. However, the perturbation velocity, integrated over such a plane, takes a constant value, positive if the plane lies on one side of the sphere and negative if it lies on the other side. It follows that the effect of all the spheres is not to alter the shearing stress at all, but to reduce the mean shear by a factor 1 – 2·5c, where c is the concentration. This suggests that Einstein's viscosity law should be altered to η = η0/(1 – 2·5c) when c is not small.
Optimum power generation from a moving plasma
Authors: Neuringer Joseph L.
Published: March 2006

The possibility exists of directly using the plasma, resulting from a controlled fusion reaction, to generate electricity by electromagnetic induction. Two special cases of a more general problem are considered here: (1)the extraction of optimum power from the steady one-dimensional flow of an incompressible inviscid plasma across a uniform transverse magnetic field in an externally loaded channel of arbitrarily varying cross-section, and (2) the extraction of optimum power from the steady one-dimensional flow of a compressible inviscid plasma across a uniform transverse magnetic field in a channel of uniform cross-section. In each case, the magnitude of the required external loading at optimum power operation is determined as a function of the parameters which characterize the hydromagnetic interaction. Also determined are the magnitudes of the terminal voltate, power, fluid mechanical to electrical conversion efficiency, and the variation of the fluid dynamical variables along the channel at optimum power.
Analysis of vibrational relaxation regions by means of the Rayleigh-line method
Authors: Johannesen N. H.
Published: March 2006

The physics of shock-waves with vibrational relaxation regions is recapitulated, and it is shown that exact methods of analysis can be developed from the classical Rayleigh-line equations by treating the real gas as an ideal gas with heat transfer. By using these methods to analyse experimental records of density distributions in relaxation regions, a large number of local values of the relaxation frequency, rather than a single over-all value, may be obtained from each shock-wave record.
Comparison of exact and approximate methods for analysing vibrational relaxation regions
Authors: Blythe P. A.
Published: March 2006

The validity of various solutions for the vibrational relaxation region in shock-waves, and of the assumptions on which they are based, has been assesed by comparison with an exact solution obtained by numerical integration of the relaxation equation, and also by use of the Rayleigh-line equations. Estimates of errors in the values of the relaxation frequency, determined by means of these solutions, are given.
A further note on the speed of floating bodies in a stream
Authors: Francis J. R. D.
Published: March 2006

In an earlier contribution (Francis 1956), a report was made of the speed of small solid bodies floating in the upper layers of a free surface stream. The bodies were cylinders of several diameters floating with their axes vertical and ballasted to the same draft. All the floats travelled at the same speed in the long, wide stream which was of constant depth and was strongly sheared, and this speed was the mean speed of the upper layers of the stream. It was pointed out that this result is unexpected, since the solid boundaries of the floats prevent turbulent interchange there, so that the floats are not locked to the stream in the same way as the corresponding volume of turbulent water would be locked. Thus the floats would be expected to travel a little faster than the stream, large diameter floats travelling faster than small floats.
The effect of a very strong magnetic cross-field on steady motion through a slightly conducting fluid
Authors: Ludford G. S. S.
Published: March 2006

The flow engendered by the steady motion of a cylindrical insulator through an inviscid, incompressible fluid of small conductivity σ is not close to potential flow when the applied magnetic cross-fieldH0is sufficiently strong. Here we determine the limiting form of this flow as σ → 0 with$\sigma H^2_0 \rightarrow \infty$, the latter representing the ponderomotive force.

The limit equations do not have a unique solution, but it is possible to make a selection by taking into account the inertia of the fluid during the limiting process, i.e. without recourse to considerations of how the motion was set up from rest. The forces on the cylinder are found to be asymptotically proportional to$\surd {\sigma} H_0$.

The case of an elliptic cylinder and that of a flat plate are worked out in detail.
Unsteady interaction of a shock wave with a cellular vortex field
Authors: Werner J. E.
Published: March 2006

The transient effects generated when a shock wave is suddenly disturbed by a field of cellular vortices have been studied. Both the pressure disturbance on the shock and the local shock velocity are found to be strong functions of the cell geometry. Disturbances are resolved into transient components and sinusoidal components of constant amplitude. The transients are found to die out as t−3/2, t being the interaction time, except for one particular case of the cell geometry for which they diminish as t−1/2. Furthermore, the analysis indicates that the initial magnitude of the transient components may be quite appreciable in comparison with the sinusoidal component. The theory is extended to treat the convection through the shock of a single column of vortex cells.
The theory of the jet-flap for unsteady motion
Authors: Spence D. A.
Published: March 2006

Linearized methods developed in earlier papers (Spence 1956, 1961) are used to discuss the non-stationary flow of a wing with a jet-flap. We consider a thin twodimensional wing at zero incidence in a steady stream of speed U, with a thin jet emerging parallel to the chord at the trailing edge, and study the motion following an instantaneous deflexion of the jet through an angle τ0. If the momentum-flux coefficient CJ of the jet is [Lt ] 4, the governing equations can be put in a form in which CJ does not appear explicitly, and a similarity solution then gives the shape of the jet at small times t from the start of the motion as a function of $(x -c)\mu ^{-\frac {1}{3}}t^{-\frac {2}{3}}$, where x= c is the trailing edge and $\mu = \frac{1}{2}C_J$. The solution is obtained from a certain third-order integro-differential equation, by constructing the Mellin transform of the non-dimensional shape. When t is large the jet near the wing approaches the shape given by the known results for steady flow, but its shape at distances of the order of Ut downstream changes diffusively under the action of the starting vortex. A similarity solution is also found for the flow in this region in terms of $(x -c)\mu ^{-\frac {1}{3}}t^{-\frac {2}{3}}$, without restriction to small μ. Expressions for the lift coefficient at small and large times are found, and the case of an oscillating deflexion angle is treated by the same methods.
On the behaviour of liquid dispersions in mixing vessels
Authors: Shinnar Reuel
Published: March 2006

The present paper is concerned with the conditions of flow in tanks containing stirred fluids. An attempt is made to apply the theoretical concepts of local isotropy to explain the behaviour of liquid in liquid dispersions, subjected to turbulent agitation. Relations describing quantitatively the influence of turbulence on both break-up and coalescence of individual droplets are derived and are compared with experimental evidence. A special type of dispersion is described in which droplet size is controlled by the prevention of coalescence due to turbulence. The dependence of droplet size on energy dissipation per unit mass, as predicted by the theory of local isotropy, is put to an experimental test using geometrically similar vessels of different sizes.

Though the results are not entirely conclusive, experimental evidence suggests that the hypothesis of locally isotropic flow may be applicable to the flow conditions described in the paper, and that statistical theories of turbulence can be of practical value in estimating droplet sizes in agitated dispersions.
A study of the magnetohydrodynamic boundary layer on a flat plate
Authors: Glauert M. B.
Published: March 2006

This paper is concerned with the boundary layer on a semi-infinite flat plate in a uniform stream of conducting fluid, with a magnetic field in the stream direction such that the Alfvén speed is less than the undisturbed fluid speed. Series solutions are derived which are applicable for large and small values of the electrical conductivity, and which give a guide as to the validity and limitations of theories which assume the fluid to have infinite or zero conductivity.
The boundary layer on a flat plate in a stream with uniform shear
Authors: Murray J. D.
Published: March 2006

The incompressible laminar boundary layer on a semi-infinite flat plate is considered, when the main stream has uniform shear. A solution is obtained for the first two terms of an asymptotic solution for small viscosity. It is shown that one of the principal effects of free-stream vorticity is to introduce a modified pressure field outside the boundary-layer region.
Measurement of interfacial structure for co-current air–water flow
Authors: Lilleleht Lembit U. , Hanratty Thomas J.
Published: March 2006

A method for measuring the interfacial structure between a co-current air-water flow using the absorption of light is described. Measurements of the root-meansquared displacement and the frequency spectrum are presented. The use of a Gaussian model to describe the interface is explored.
The force on a sphere moving through a conducting fluid in the presence of a magnetic field
Authors: Reitz J. R. , Foldy L. L.
Published: March 2006

The force on a sphere moving through an inviscid, conducting fluid in the presence of a uniform magnetic field B0 is calculated for the low-conductivity case where the hydrodynamic motion deviates only slightly from potential flow. The magnetic Reynolds number is assumed small. The force on the sphere is found to consist of both a drag and a deflective component which tends to orient its motion parallel to a magnetic field line; if the sphere's velocity is V, the force may be written
$\bf {R} = -AB^2_0\bf {V} + \bf C(V.B_0)B_0$
where the coefficients A and C depend on the conductivities of both sphere and fluid. The coefficients are evaluated by calculating the Joule dissipation for particular orientations of V relative to B0. In one case the force is also calculated directly from the perturbed pressure distribution in the fluid. In an analogous way, a spinning sphere in a conducting fluid experiences both resistive and gyroscopic torques.
A dispersion relation for waves of finite amplitude in a two-stream plasma
Authors: Kahn F. D.
Published: March 2006

A dispersion relation is derived for plane space-charge waves of finite amplitude in a plasma containing two oppositely charged streams of particles. The relation may be expressed simply in parametric form; it can also be quite well approximated, in two different ranges of amplitude, by expressions for the wavelength in terms of the maximum variation of the electrostatic potential.
Spectral flatness factor and ‘intermittency’ in turbulence and in non-linear noise
Authors: Kennedy D. A. , Corrsin S.
Published: March 2006

The flatness factor F of the signal transmitted through a band-pass filter has been measured for the turbulence in a free shear layer and for a squared Gaussian noise. They both show flatness factor increasing with centre frequency fc. In the turbulence, band-passed signals look intermittent and have larger F than the full signal, but in the squared noise, band-passed signals all have smaller F than the full signal although they look more intermittent.

It is shown analytically that the derivative of a smoothed, squared Gaussian noise may have flatness factor either greater or less than the undifferentiated signal.
Orifice flow at high Knudsen numbers
Authors: Narasimha Roddam
Published: March 2006

Several interesting features of the flow field in free-molecule flow through an orifice are discussed. An estimate is then made of the deviation of the mass flow $\dot{m}$ through the orifice from its limiting free-molecule value $\dot{m}$ for small departures from the limit. Using an iteration method proposed by Willis, it is shown that this deviation is of the first order in ε, the inverse Knudsen number, defined as the ratio of the radius of the hole to the mean free path in the gas at upstream infinity. An estimate of the coefficient is obtained making some reasonable assumptions about the three-dimensional nature of the flow, and the value so derived, giving $\dot{m}=\dot{m}(1+0.25\epsi)$, shows fair agreement with the measurements of Liepmann. It appears that ‘nearly’ free-molecular conditions prevail up to ε ∼ 1.0.
Interaction between gravity waves and a shear flow
Authors: Hughes B. A. , Stewart R. W.
Published: March 2006

A series of experiments has been undertaken in which three major properties of a surface tension-gravity wave system have been examined. The results of these experiments have been compared with existing theories. The three properties are: (i) viscous decay in the absence of mean flow, the relevant theory being given in Lamb (1932, § 348); (ii) propagation velocities in the presence and absence of flow (Lamb 1932, § 267), and (iii) the change of wave energy on crossing a stable Couette shear flow. The measurements in the last case were compared with two theories, one obtained from the Navier–Stokes equations including terms up to second order in wave slope, the other, following previous authors, obtained on the assumption that any direct interaction of the waves with the shear flow is negligible. According to the theory obtained from the Navier–Stokes equations, the divergence of surface wave energy is equal to the rate of change of wave energy due to the interaction between the mean flow and the wave system plus the rate of change of wave energy due to viscous decay.

An optical system was used to measure the maximum wave slopes, the wave-numbers and the shear velocities.

Results indicate that an anomalous region of wave properties exists for wave-numbers near 2.7 cm−1. For a set of data in which the wave-numbers were always less than 1.8 cm−1, it was found that the viscous decay rate and the propagation laws agree with theory to within the experimental error, and the interaction measurements fit the theory with the non-linear term included rather than the traditional theories.