bluuebunny/crossref_metadata_2025 huggingface dataset:
Climb of a bore on a beach. Part 1. Uniform beach slope
Authors: Ho D. V. , Meyer R. E.
Published: March 2006

The shoreward travel of a bore into water at rest on a beach of uniform slope is studied to elucidate why, in a class of problems—mainly gas-dynamical ones involving non-uniform shock propagation—similarity solutions seem to act like magnets attracting other solutions. For the shallow-water problem, the real magnet is shown to be the shore singularity of the governing differential equations. The shore singularity of the solution is shown to be a directional singularity of the water acceleration, for a fairly wide range of conditions, and a rather detailed asymptotic approximation for the bore development near shore is deduced.
The growth of Taylor vortices in flow between rotating cylinders
Authors: Davey A.
Published: March 2006

In flow between concentric rotating circular cylinders, it was shown by Taylor (1923) that instability may occur in the form of toroidal vortices spaced regularly along the axis. When the vortex motion occurs additional torque is required to keep the cylinders in motion at given speeds. Stuart (1958) used an energy-balance method, in the case when the annular gap is small compared with the radius, to estimate the additional torque and the associated finite amplitude attained by the vortices. He included the effect of distortion of the mean motion, but ignored the generation of harmonics of the fundamental mode and the distortion of the velocity associated with the fundamental mode. It is now known that these are not valid mathematical approximations and a rigorous perturbation expansion is developed here to remedy the deficiency. The analysis is valid for any gap width and any angular speeds of the containing cylinders, but requires the amplification rate of the disturbance to be small.

Numerical results using a digital computer are obtained for the shape and amplitude of the vortices in three cases: (i) when the outer cylinder has twice the radius of the inner one and is kept at rest, (ii) when the gap is small and the cylinders rotate with nearly the same speeds, and (iii) when the gap is small and the outer cylinder is kept at rest. The equilibrium amplitude obtained in the last case is substantially the same as that found by Stuart.

The results for cases (i) and (iii) give close agreement with the experimental values obtained by Taylor (1936) and Donnelly (1958) for the torque required to keep the inner cylinder rotating with constant speed while the outer one is at rest, for a certain range of speeds. In the small-gap problem it is shown that the equilibrium amplitude is almost proportional to 1 − m, where m is the ratio of the angular speeds of the outer and inner cylinders.
Large-amplitude compression waves in an adiabatic two-fluid model of a collision-free plasma
Authors: Morton K. W.
Published: March 2006

The development of large amplitude compression waves in a collision-free plasma is studied by considering the motion of a plane piston into a uniform stationary plasma containing a magnetic field parallel to the plane of the piston. The adiabatic two-fluid equations are solved by finite-difference methods and the form of the waves after a long time is compared with the possible steady-state solutions.

A generalized discontinuous solution of the steady-state equations is found for sufficiently high Mach numbers. At the highest Mach numbers this leads to a constant state at the piston; while at lower speeds a wave train results whose amplitude increases as the speed decreases. In each of these cases the numerical solutions of the time-dependent equations converge rapidly to the steady-state solutions. At still lower speeds, where the solitary-wave solution exists, the situation is less clear.
On the analogy between the transport of vorticity and heat in laminar boundary layers
Authors: Riley N.
Published: March 2006

The analogy between the transport of heat and vorticity when the Prandtl number is unity is used to provide a simple complementary solution of the boundary-layer energy equation for plane flow. The solution is extended to apply to axisymmetric boundary layers by suitably stretching the co-ordinate normal to the wall. Several applications of the solution are discussed.
A study of the combined effect of thermal radiative transfer and a magnetic field on the gravitational convection of an ionized fluid
Authors: Murgai M. P. , Khosla P. K.
Published: March 2006

The effect of radiative transfer on the thermal stability of an ionized fluid, in the presence of uniform vertical magnetic field has been examined from hydromagnetic approximations. Two asymptotic cases (i) when the fluid is optically thin and (ii) when it is optically thick, have been examined in detail. The principle of exchange of stabilities and the concept of over-stability have been discussed and the physical conditions under which the former will hold, obtianed. Also the conditions as to which type of instability will arise first are derived and it has been shown that in the presence of large magnetic field over-stability arises earlier than convection under the first approximation.
On shear flow past flat plates
Authors: Mark Richard M.
Published: March 2006

The boundary layer on a semi-infinite flat plate placed in a two-dimensional, unbounded, steady, constant shear flow of a viscous incompressible fluid is examined on the basis of the constant-pressure assumption. An asymptotic solution is obtained first for large vorticity numbers. Then an approximate solution is found for arbitrary vorticity numbers that gives good agreement with exact calculations for the extreme cases of small and large vorticity numbers. The present calculations are limited to the boundary layer on the top side of the plate only.
Experimental investigation of the penetration of a high-velocity gas jet through a liquid surface
Authors: Banks Robert B. , Chandrasekhara D. V.
Published: March 2006

This investigation is concerned with the phenomenon of a gas jet impinging on and penetrating into a liquid. The study has been restricted to the cases of circular and plane jets penetrating a liquid at right angles. Both ‘free streamline’ and turbulent jets were considered. The phenomenon was analysed from two viewpoints. The first, a stagnation-pressure analysis, related the depth of the surface depression or cavity to the stagnation pressure based on the centre-line velocity of the jet in the neighbourhood of the surface. The second, a displaced-liquid analysis, related the weight of the liquid displaced from the cavity to the momentum of the jet.

Numerous experiments were conducted in which the cavity depth, diameter or width, and peripheral lip height were measured. The role of surface tension in affecting the cavity depth was considered and the phenomenon of drop formation was examined. Some attention was given to the case of a plane jet impinging on a moving liquid. It was found that the experimental data fit into the framework of these analyses quite consistently.
The vertical diffusivity and mean velocity of particles in a horizontal water pipe
Authors: Barnard B. J. S. , Binnie A. M.
Published: March 2006

Small spheres of the same size but of relative density varying from 0·92 to 1·25 were injected in turn into a horizontal water pipe, in which the flow was turbulent and the mean velocity was constant. A cross-section near the outlet was illuminated; the positions of the spheres as they crossed it were measured by photography, and the relation was established between the terminal velocity of the of the spheres in water and the vertical diffusivity. The velocity of the spheres along the pipe was found to be somewhat different in the galvanized steel and Perspex lengths of which the pipe was composed. The dispersion of the times of transit of the spheres increased slightly with their densisty. For purposes of comparison the theoretical velocity along the pipe was also calculated from the photographic measurements.
Lagrangian similarity hypothesis applied to diffusion in turbulent shear flow
Authors: Cermak J. E.
Published: March 2006

The concept suggested by Batchelor that motion of a marked particle in turbulent shear flow may be similar at stations downstream from the point of release is applied to a variety of diffusion data obtained in the laboratory and in the surface layer of the atmosphere. Two types of shear flow parallel to a plane solid boundary are considered. In the first case mean velocity is a linear function of logz(neutral boundary layer) and in the second case the mean velocity is slightly perturbed from the logarithmic relationship by temperature variation in thez-direction (diabatic boundary layer). Besides the parameters introduced in previous applications of the Lagrangian similarity hypothesis to turbulent diffusion, the ratio of source height to roughness lengthh/z0is shown to be of major importance. Predictions of the variation of maximum ground-level concentration for continuous point and line sources and the variation of plume width for a continuous point source with distance downstream from the source agree with the assorted data remarkably well for a range of length scales extending over three orders-of-magnitude. It is concluded that results from application of the Lagrangian similarity hypothesis are significant for the laboratory modelling of diffusion in the atmospheric surface layer.
Rocket exhaust impingement on a ground surface
Authors: Yoshihara Hideo
Published: March 2006

The impingement of a rocket jet, exhausting into a vacuum, onto a solid surface is examined using the Newtonian approximation to analyse the transonic region. The jet exhaust into an unbounded vacuum required for this analysis is simplified as a quasi-radial flow using an exact calculation as a basis. Two examples are calculated giving the shock detachment distance and the ground pressures as a function of the rocket altitude.
Resonant effect of plasma waves on charged particles in a magnetic field
Authors: Dungey J. W.
Published: March 2006

Resonances are discussed between electrons and protons and waves of whistler and hydromagnetic types. The conditions of resonance are investigated. Approximations for the effects on the particles are obtained. The occurrence of a ‘trapping’ phenomenon is demonstrated and the effect on velocity distributions is discussed.
Experiments with a self-propelled body submerged in a fluid with a vertical density gradient
Authors: Schooley Allen H. , Stewart R. W.
Published: March 2006

It is shown that the turbulent wake of a self-propelled body moving in a fluid with a vertical density gradient is considerably different than of the same body moving in a fluid having no density gradient. In the uniform density case, the turbulent mixed fluid behind the body expands into an irregular conical shape. In the case of a density gradient, the initial expansion of the mixed fluid is quickly followed by a collapse in the vertical direction which is accompanied by a further spreading in the horizontal direction. This phenomenon is caused by the force of gravity. The volume of fluid behind the self-propelled body has a more or less constant density due to mixing. Thus, it is forced to seek its own density level in the undisturbed fluid.

The collapsing vertical wake is shown to be an efficent generator of internal waves, many of high order. These manifest themselves in surface movements.

The assumption that the internal waves are damped only by viscosity, not by turbulence, leads to results in general accord with the observations.
The Constant-Mach-number MHD generator
Authors: Swift-Hook D. T. , Wright J. K.
Published: March 2006

It is shown that the optimum design of duct in a magnetohydrodynamic generator is close to the one in which the flow Mach number remains constant. This constant-Mach-number generator is analysed in some detail and it is shown that the optimum Mach number can be defined to within a few percent. For a γ of 1·25, this optimum is near 0·85. For very short ducts, the maximum power output is obtained near matched-load conditions but for rather longer ones maximum total power output is obtained by working as close to short-circuit conditions as is practicable. Against this, the minimum compressor requirements are found by working as close to open-circuit conditions as is practicable, and so a compromise must be reached for optimum overall generator design as far as load conditions are concerned. This will probably give an internal ohmic loss in the fluid of about one-third of the total output. Curves are presented which enable the optimum Mach number to be determined with greater precision when the optimum load conditions have been selected.
Similarity rules for isothermal bubble growth
Authors: Langlois W. E.
Published: March 2006

A normalized formulation of the problem of isothermal bubble growth, dominated by viscosity and diffusion, reveals that in its full generality the problem involves eight dimensionless parameters. Limiting cases for extreme values of each of these parameters are investigated.
Heat transfer across rough surfaces
Authors: Owen P. R. , Thomson W. R.
Published: March 2006

It is argued that the heat transfer between a roughened surface and a stream of incompressible fluid flowing over it is dependent on both the viscosity and thermal conductivity of the fluid even when the roughness is large enough for viscosity to have ceased to affect the skin friction.

Concentrating on closely spaced roughness, sufficiently large for the skin friction to be independent of Reynolds number, a simple model is constructed of the flow near the surface. It consists of horseshoe eddies which wrap themselves round the individual excrescences and trail unsteadily downstream; the eddies are imagined to scour the surface and thereby to transport heat between the surface and the more vigorous flow in the neighbourhood of the roughness crests. Taken in conjunction with Reynolds analogy between temperature and velocity distributions in the fluid away from the surface, the model leads to an expression for the rate of heat transfer which contains a function of the roughness Reynolds number and the Prandtl number of the fluid whose detailed form is found by appeal to the limited experimental data available. An order-of-magnitude argument suggests that the functional form established empirically is consistent with the assumed model of the flow close to the surface.

The object of the work is to establish a basis for the analysis of experimental data and for their extrapolation with respect to Reynolds number and Prandtl number.
On the stability of a plane vortex sheet with respect to three-dimensional disturbances
Authors: Fejer J. A. , Miles John W.
Published: March 2006

The previously established criterion for the stability of a vortex sheet with respect to two-dimensional disturbances in a compressible fluid is extended to three-dimensional disturbances, and it is shown that disturbances travelling at sufficiently oblique angles with respect to the undisturbed flow are unstable. Slip-line instability downstream of a Mach reflexion is discussed briefly.
The mean velocity profile in three-dimensional turbulent oundary layers
Authors: Hornung H. G. , Joubert P. N.
Published: March 2006

The mean velocity distribution in a low-speed three-dimensional turbulent boundary-layer flow was investigated experimentally. The experiments were performed on a large-scale model which consisted of a flat plate on which secondary flow was generated by the pressure field introduced by a circular cylinder standing on the plate. The Reynolds number based on distance from the leading edge of the plate was about 6 x 106.

It was found that the wall-wake model of Coles does not apply for flow of this kind and the model breaks down in the case of conically divergent flow with rising pressure, for example, in the results of Kehl (1943). The triangular model for the yawed turbulent boundary layer proposed by Johnston (1960) was confirmed with good correlation. However, the value ofyuτ/vwhich occurs at the vertex of the triangle was found to range up to 150 whereas Johnston gives the highest value as about 16 and hence assumes that the peak lies within the viscous sublayer. Much of his analysis is based on this assumption.

The dimensionless velocity-defect profile was found to lie in a fairly narrow band when plotted againsty/δ for a wide variation of other parameters including the pressure gradient. The law of the wall was found to apply in the same form as for two-dimensional flow but for a more limited range ofy.
On the non-linear energy transfer in a gravity-wave spectrum. Part 3. Evaluation of the energy flux and swell-sea interaction for a Neumann spectrum
Authors: Hasselmann K.
Published: March 2006

The energy transfer due to non-linear interactions between the components of a gravity-wave spectrum discussed in Parts 1 and 2 of this paper is evaluated for a fully and partially developed Neumann spectrum with various spreading factors. The characteristic time scales of the energy transfer are found to be typically of the order of a few hours. In all cases the high frequencies and the low-frequency peak are found to gain energy from an intermediate range of frequencies. The transfer of energy to very low frequencies and to waves travelling at large angles to the main propagation direction of the spectrum is negligible. Computations are presented also for the rate of decay of swell interacting with local wind-generated seas (represented by a Neumann spectrum). An appreciable decay is found only for swell frequencies in the same range as those of the local sea.
On a pulsating jet from the end of a tube, with application to the propulsion of certain aquatic animals
Authors: Siekmann J.
Published: March 2006

The present paper discusses the hydrodynamics and propulsive properties when a jet of fluid is ejected from the opening of a tube. Formulas for the calculation of the thrust are provided and the basic equations for the horizontal rectilinear motion of a rigid torpedo-like body are studied in some detail. The results may be applied to investigate in an elementary way the locomotion of certain aquatic animals.
The effect of a strong magnetic field on two-dimensional flows of a conducting fluid
Authors: Childress Stephen
Published: March 2006

The motion of a viscous, electrically conducting fluid past a finite two-dimensional obstacle is investigated. The magnetic field is assumed to be uniform and parallel to the velocity at infinity. By means of a perturbation technique, approximations valid for large values of the Hartmann number M are derived. It is found that, over any finite region, the flow field is characterized by the presence of shear layers fore and aft of the body. The limit attained over the exterior region represents the two-dimensional counterpart of the axially symmetric solution given by Chester (1961). Attention is focused on a number of nominally ‘higher-order’ effects, including the presence of two distinct boundary layers. The results hold only when M [Gt ] Re; Re = Reynolds number. However, a generalization of the procedure, in which the last assumption is relaxed, is suggested.
An experimental investigation of a two-layer inviscid shock cap due to blunt-body nose injection
Authors: Baron Judson R. , Alzner Edgar
Published: March 2006

Blunt-body solutions for suspersonic flow usually concern closed body surfaces. This paper reports on an experimental investigation of a two-layer shock cap and indicates the existence of a predictable contact surface separating the layers. The inner layer was generated by injecting air through a contoured axisymmetric channel on a blunt body so as to simulate a hemispherical contact surface in a Mach number 4.8 flow.

Results show the existence of the contact surface and the influence of a range of mass-injection rates upon the displacement of the bow shock and contact surface from the body.
The magnetohydrodynamic flow past a non-conducting flat plate in the presence of a transverse magnetic field
Authors: Dix D. M.
Published: March 2006

The general character of the magnetohydrodynamic flow past a non-conducting flat plate in the presence of transverse magnetic fields is analysed in some detail. The appropriate extension of the Rayleigh problem to the magnetohydrodynamic case is shown to yield solutions which correctly predict some features of the steady flow past a semi-infinite flat plate; in addition, it is shown that the knowledge of these significant features permits an easy evaluation of their magnitudes in other extensions of the Rayleigh problem. The flow past a semi-infinite flat plate is analysed by two methods. First, by linearizing the governing equations and incorporating the assumption of a low ratio of viscous to magnetic diffusivity, the results for skin friction and the normal component of magnetic field at the plate are obtained and are shown to be useful in interpreting the character of these low conductivity flows. Secondly, the complete set of governing equations is formulated as a finite difference problem and solved numerically on a digital computer. The results obtained, in addition to demonstrating feasibility of the numerical calculations, show that the disturbance produced by the plate is no longer confined to a thin viscous layer if the ratio of viscous to magnetic diffusivity is greater than 10−2, but that an appreciable Alfvén type disturbance is excited.
An experiment to measure the recombination rate of oxygen
Authors: Wilson J.
Published: March 2006

The feasibility of an experiment to measure the recombination rate of oxygen is examined using the ideal-dissociating-gas model. The experiment is to be performed in a shock tube, the shock-heated (and dissociated) gas being cooled by passing it through a Prandtl-Meyer expansion, and then allowed to recombine in a constant-area channel. At appropriate densities and shock Mach numbers it is found that recombination takes place in a distance suitable for a laboratory experiment.

Using this technique, the recombination rate of oxygen has been measured at 2700 ˚K. To determine the recombination rate, the absorption of ultraviolet light at a wavelength of 2283 å measured 11 cm downstream of the expansion was compared with absorptions calculated for various values of the recombination rate constant.

The measured value of the recombination rate constant of oxygen is in agreement with values calculated from dissociation rate measurements.
The flow in compound jets
Authors: Lennox S. C. , Pack D. C.
Published: March 2006

The Wiener-Hopf technique is applied to solve the linearized problem of a two-dimensional compound gas jet, i.e. a jet embedded in a gaseous stream of finite width. The solution is found for all combinations of supersonic and subsonic flows in jet and stream. The general nature of the solution when only one of the flows is supersonic varies according as the value of a certain quantity mk, depending upon the gas constants, Mach numbers and widths of streams, is greater than or less than unity. When mk= 1 the solution appears to be invalid and it is suggested that, in this critical case, a steady flow (regarded as the limit in time of an unsteady flow) may not exist. It is further shown that the solution propounded by Pai (1952) for a supersonic jet embedded in a subsonic stream is simply the asymptotic form of the general solution. The findings of Pack (1956) for a supersonic jet in a supersonic stream are confirmed and extended.
Convection in a saturated porous medium at large Rayleigh number or Peclet number
Authors: Wooding R. A.
Published: March 2006

When the dimensions of a convective system in a saturated porous medium are sufficiently great, diffusion effects can be neglected except in regions where the gradients of fluid properties are very large. A boundary-layer theory is developed for vertical plane flows in such regions. In special cases, the theory is equivalent to that for laminar incompressible flow in a two-dimensional half-jet, or in a plane jet or round jet, for which similarity solutions are well known.

A number of experiments have been performed using a Hele-Shaw cell immersed in water, with a source of potassium permanganate solution located between the plates. At very small values of the source strength, a flow analogous to that of a plane jet from a slit is obtained. The distance advanced by the jet front, or cap, is measured as a function of time, and the velocity is found to be nearly proportional to the velocity of the fluid on the axis of the steady jet behind the cap, as given by the similarity law of Schlichting and Bickley. At large values of the source strength, a two-dimensional ‘broad jet’ of homogeneous solution descending under gravity is produced; the shape of the flow region can be calculated with little error from potential theory, neglecting the effect of the mixing layers.

A possible example of a mixing layer observed in a geothermal region is examined. The theoretical form of the temperature distribution is calculated numerically, taking into account the large viscosity variation with temperature and also the possibility of a large permeability variation. These effects are found to have less influence upon the solution than might have been expected. Quantitative values obtained for the physical parameters are consistent with other geophysical observations.
An experimental study of the instability of the laminar Ekman boundary layer
Authors: Faller Alan J.
Published: March 2006

This study concerns the stability of the steady laminar boundary-layer flow of a homogeneous fluid which occurs in a rotating system when the relative flow is slow compared to the basic speed of rotation. Such a flow is called an Ekman boundary-layer flow after V. W. Ekman who considered the theory of such flows with application to the wind-induced drift of the surface waters of the ocean.

Ekman flow was produced in a large cylindrical rotating tank by withdrawing water from the centre and introducing it at the rim. This created a steady-state symmetrical vortex in which the flow from the rim to the centre took place entirely in the shallow viscous boundary layer at the bottom. This boundary-layer flow became unstable above the critical Reynolds number$Re_c = vD|v = 125 \pm 5$wherevis the tangential speed of flow,$D = (v| \Omega)^{\frac {1}{2}}$is the characteristic depth of the boundary layer,vis the kinematic viscosity, and Ω is the basic speed of rotation. The initial instability was similar to that which occurs in the boundary layer on a rotating disk, having a banded form with a characteristic angle to the basic flow and with the band spacing proportional to the depth of the boundary layer.
On plane flow of a gas with finite electrical conductivity in a strong magnetic field
Authors: Cowley M. D.
Published: March 2006

The principal object of study is plane flow over bodies with a sharp apex at Mach numbers greater than unity. The magnetic field is assumed to be uniform, rectilinear, and parallel to the undisturbed stream. Flow behaviour near the apex of a wedge is investigated by the method of characteristics. It is found that for small wedge angles an attached shock attenuates initially with distance from the apex, but for larger wedge angles the shock grows stronger.

The structure of a slow magneto-gasdynamic shock is investigated for the case of strong magnetic field and small electrical conductivity. The streamlines are displaced within the shock although the initial and final flow directions are the same. An ordinary gasdynamic shock may occur on the upstream side of the transition. The shock structure theory gives a solution for the flow near the apex of a certain class of bodies.

For the study of slow shock structure, it is shown that the transition is described by a curve in the (F, H)-plane. F is the sum of pressure and momentum flux in the direction of variation; H is the sum of enthalpy and kinetic energy due to the velocity component in the direction of variation. General properties of the (F, H)-plane are found for a gas whose equation of state obeys the conditions of Weyl (1949). Flow behaviour on the transition curve is then determined. The theory of the (F, H)-plane can be used in the study of other one-dimensional processes in magneto-gasdynamics.
Some mass transfer effects on the wall jet
Authors: Fox Herbert , Steiger Martin H.
Published: March 2006

The wall jet with suction or injection is investigated; an analysis under conditions corresponding to similar flows is shown to reduce to an eigenvalue problem. Asymptotic solutions valid far from the surface are used to initiate the integration and circumvent the usual iteration associated with the two-point boundary-value problem. Typical solutions for various rates of suction and injection are obtained. It is found that the skin friction decreases with increasing rate of suction. Representative thermal solutions are obtained for Prandtl and Lewis numbers equal to one, under the special condition that the surface temperature is equal to the ambient temperature or that the enthalpy varies monotonically from the surface value to the ambient value.
On the mechanics of a magnetohydrodynamical twin wake
Authors: Sakurai Takeo
Published: March 2006

In this paper, we consider the elementary processes involved in the appearance of a simple twin wake in the two-dimensional steady aligned flow of an electrically conducting viscous incompressible fluid in a uniformaly applied magnetic field. Fundamental relations between the twin wake and its elementary process are generally discussed, and the corresponding initial-value problem is formulated. Then, the solution of the initial-value problem corresponding to the above simple twin wake is obtained, and two limiting cases with the magnetic Prandtl number near one and zero (or infinite) are discussed in detail. In both cases, it is found that negative vorticity appears in between the main positive vorticity associated with the two Alfven spots. This fact gives some clue to the understanding of the property of twin wakes. As an application, the crossed-flow case is also discussed, and a conjecture upon the vorticity distribution is made.
On the stability of viscous plane Couette flow
Authors: Deardorff J. W.
Published: March 2006

The problem of the stability of plane Couette flow to infinitesimal disturbances is carried numerically to larger Reynolds numbers than heretofore. The flow is definitely stable up to R = 1430, although at Reynolds numbers in this vicinity plane Couette flow has been observed experimentally to be turbulent. Observations on boundary-layer instability suggest this to be the source of turbulence in plane Couette flow channels.
The boundary layer on a spherical gas bubble
Authors: Moore D. W.
Published: March 2006

The equations governing the boundary layer on a spherical gas bubble rising steadily through liquid of small viscosity are derived. These equations are linear are linear and are solved in closed form. The boundary layer separates at the rear stagnation point of the bubble to form a thin wake, whose structure is determined. Thus the drag force can be calculated from the momentum defect. The value obtained is 12πaaUμ, where a is the bubble radius and U the terminal velocity, and this agrees with the result of Levich (1949) who argued from the viscous dissipation in the potential flow round the bubble. The next term in an expansion of the drag in descending fractional powers of R is found and the results compared with experiment.
Instability of a surface of discontinuity of velocity in a parallel uniform magnetic field
Authors: Mallick D. D.
Published: March 2006

The problem described by the title is investigated when the magnetic field is uniform and parallel to the velocity on the two sides of a surface of discontinuity of velocity in an electrically conducting inviscid fluid. The secular equation depends on two parameters β and N, where β is the ratio of magnetic Reynolds number to dimensionless wave number and N is the ratio of the magnetic to the kinetic energy of the fluid. It is found that the flow is unstable for all values of β and N.
Measurements of helical flow of a strong electrolyte with and without a transverse magnetic field
Authors: Boedeker Laurence R. , Covert Eugene E.
Published: March 2006

This note describes the slow magneto-hydrodynamic flow of hydrochloric acid in a helix. At very low Reynolds number a transverse magnetic field is found to retard the flow in agreement with existing theory and with existing experimental results obtained using mercury. At higher Reynolds numbers where secondary flow in a helix becomes important the transverse magnetic field is found to reduce this secondary flow.
On the flow of an elastico-viscous liquid in a curved pipe under a pressure gradient
Authors: Thomas R. H. , Walters K.
Published: March 2006

Consideration is given to the flow of an idealized elastico-viscous liquid in a curved pipe under a pressure gradient. By using the series expansion method of Dean (1927, 1928) in powers of a/R where a is the radius of the pipe and R the radius of curvature of its ‘central line’, it is shown that the general nature of the motion is similar to that of the motion of a Newtonian viscous liquid, the liquid elements moving along the pipe in two sets of spirals separated by the central plane. However elasticity of the type considered could strongly affect the pitch of these spirals. To the approximation considered, the flow pattern of the elastico-viscous liquid depends only on the limiting (zero-shear-rate) viscosity η0 and the first moment, K0, of the distribution of relaxation times. The corresponding stress components involve also the second moment of this distribution.

It is also shown that the presence of elasticity in the liquid increases the rate of discharge of the liquid.
The use of a fibre anemometer in turbulent flows
Authors: Tritton D. J.
Published: March 2006

Quartz fibre anemometers have been used (as described in subsequent papers) to survey the velocity field of turbulent free convective air flows. This paper discusses the reasons for the choice of this instrument and provides the background information for its use in this way. Some practical points concerning fibre anemometers are mentioned. The rest of the paper is a theoretical study of the response of a fibre to a turbulent flow. An approximate representation of the force on the fibre due to the velocity field and the equation for a bending beam, representing the response to this force, form the basis of a consideration of the mean and fluctuating displacement of the fibre. Emphasis is placed on the behaviour when the spectrum of the turbulence is largely in frequencies low enough for the fibre to respond effectively instantaneously (as this corresponds to the practical situation). Incomplete correlation of the turbulence along the length of the fibre is taken into account. Brief mention is made to the theory of the higher-frequency (resonant) response in the context of an experimental check on the applicability of the low-frequency theory.
Linearized pressure distributions with strong supersonic entropy layers
Authors: Sullivan R. D. , Donaldson C. DuP. , Hayes W. D.
Published: March 2006

The pressure distribution which results from the disturbance of initially plane, parallel, and constant-pressure inviscid supersonic flow in which there is a strong entropy variation near a surface is investigated. The disturbance considered may arise from a small deflection of the surface or may be the result of a simple wave impinging on the entropy layer. This linear problem has been treated previously by a somewhat different technique for transonic entropy layers by Howarth (1948), Tsien & Finston (1949), and Lighthill (1950, 1953). The results obtained in this investigation are useful principally in that they permit the general behaviour of such pressure distributions to be deduced without resort to the more general method of characteristics for rotational flows.
On the sensitivity of heat transfer in the stagnation-point boundary layer to free-stream vorticity
Authors: Sutera S. P. , Maeder P. F. , Kestin J.
Published: March 2006

Experiments have given evidence of strong sensitivity of the stagnation-point heat transfer on cylinders to small changes in the intensity of free-stream turbulence. A similar effect on local heat-transfer rates to flat plates has been measured, but only when a favourable pressure gradient is present. In this work it is theorized that vorticity amplification by stretching is a possible, and perhaps the dominant, underlying mechanism responsible for this sensitivity. A mathematical model is presented for a steady, basically plane stagnation flow into which is steadily transported disturbed unidirectional vorticity having the only orientation susceptible to stretching. The resulting velocity and temperature fields in the stagnation-point boundary layer are analysed assuming the fluid to be incompressible and to have constant properties. By means of iterative procedures and electronic analogue computation an approximate solution to the full Navier-Stokes equations is achieved which indicates that amplification by stretching of vorticity of sufficiently large scale can occur. Such vorticity, present in the oncoming flow with a small intensity, can appear near the boundary layer with an amplified intensity and induce substantial three-dimensional effects therein. It is found that the thermal boundary layer is much more sensitive to the induced effects than the velocity boundary layer. Computations indicate that a certain amount of distributed vorticity in the oncoming flow causes the shear stress at the wall to increase by 5%, while the heat transfer there is augmented by 26% in a fluid with a Prandtl number of 0.74. Preliminary computations reveal that the sensitivity of the thermal boundary layer increases with Prandtl number.
Shock-wave struture in a partially ionized gas
Authors: Grewal M. S. , Talbot L.
Published: March 2006

The structure of a shock wave in a partially ionized gas, which may be in thermal non-equilibrium ahead of the shock wave, is investigated. A method is developed to solve this problem by separating it into two parts. First, the structure of the shock wave associated with the massive particles, ions and atoms, is assumed to be of the Mott-Smith form. Then the behaviour of the electrons as they pass though this shock is analysed. Using this method, calculations are carried out for shock waves at several Mach numbers and several values of the electron-ion temperature ratio ahead of the shock. An essential feature of the shock profiles is found to be the existence of a broad zone of elevated electron temperature ahead of the electron compression region, caused by the high thermal conductivity in the electron gas.
Three-dimensional flow in cavities
Authors: Maull D. J. , East L. F.
Published: March 2006

The flow inside rectangular and other cavities in a wall has been investigated at low subsonic velocities using oil flow and surface static-pressure distributions. Evidence has been found of regular three-dimensional flows in cavities with large span-to-chord ratios which would normally be considered to have two-dimensional flow near their centre-lines. The dependence of the steadiness of the flow upon the cavity's span as well as its chord and depth has also been observed.
On the motion of liquid in a spheroidal cavity of a precessing rigid body
Authors: Stewartson K. , Roberts P. H.
Published: March 2006

The flow set up in an oblate cavity of a precessing rigid body is examined under the assumptions that the ellipticity of the spheroidal boundary of the fluid is large compared with Ω/ω and that the boundary-layer thickness is small compared with the deviations of the boundary from sphericity (ωis the angular velocity of the rigid body about the axis of symmetry,Ωis the angular velocity with which this axis precesses).

The motion of the fluid is found by considering an initial-value problem in which the axis of rotation of the spheroid is impulsively moved at a timet= 0; before that time this axis is supposed to be fixed in space, the fluid and envelope turning about it as a solid body. The solution is divided into a steady motion and transients, and, by evaluating the effects of the viscous boundary layer, the transients are shown to decay with time. The steady motion which remains consists of a primary rigid-body rotation with the envelope, superimposed on which is a circulation with constant vorticity in planes perpendicular toω× (ω×Ω), the streamlines being similarly situated ellipses.

The possible effects of the luni-solar precession on the fluid motions in the Earth's core are discussed.
A simplified theory of magnetohydrodynamic isotropic turbulence
Authors: Betchov R.
Published: March 2006

The simplest case of turbulent motion in a conductive fluid is studied. The turbulence is assumed incompressible, isotropic, homogeneous, charge invariant and free of fourth-order cumulants. The emphasis is placed on certain integrals of the correlation functions such as kinetic and magnetic energy, voticity, and current. A system of non-linear ordinary differential equations is derived which governs these integral quantities Several cases are solved numerically, illustrating the decay of ordinary turbulence, the buildup of magnetic energy by a linear or a non-linear process, the buildup of kinetic energy, as well as the destruction of vorticity by Lorentz forces.

In order to handle certain dissipative effects, a special hypothesis is introduced which seems to promote mathematical simplicity. In particular, it leads to a simple decay law very similar to the decay law of ordinary turbulence.
Boundary-layer drag in three-dimensional supersonic flow
Authors: Cooke J. C.
Published: March 2006

A general theorem for drag is given according to which the boundary-layer drag of a body is equal to the inviscid drag of the displacement surface together with a term which is given as an integral involving the ‘streamwise’ momentum and displacement thicknesses taken round the trailing edge. A less accurate result for thin slender wings is that the boundary-layer drag is equal to the line integral$\rho _\infty U^2_\infty \int \Theta d \sigma$taken round the trailing edge, where Θ is the streamwise momentum thickness. This result leads to the possibility of finding boundary-layer drag by means of a traverse round the trailing edge. The extension of the results to wings with swept trailing edges is also given.
The Cauchy–Poisson problem for a rotating liquid
Authors: Miles John W.
Published: March 2006

A semi-infinite body of liquid is in uniform rotation about a vertical axis for t < 0. A concentrated, vertical displacement of the free surface is imposed at t = 0. The motion of the free surface for t > 0 is calculated in linear approximation with the aid of Hankel and Laplace transformations, together with an intermediate transformation to parabolic co-ordinates. The result appears as an integral superposition of dispersive waves that divides naturally into two parts, corresponding to waves of the first and second class, with angular frequencies that are respectively greater or less than twice the angular speed of rotation. The waves of the first class, which are qualitatively similar to those in the classical (Cauchy–Poisson) problem, are found to dominate the asymptotic representation, as obtained through a stationary-phase approximation. The analysis is carried out in such a way as to separate the effects of Coriolis acceleration and free-surface curvature. Attention is focused on concave surfaces, such as would be realized in a laboratory experiment, but it is pointed out that striking differences exist between the dispersion laws for concave and convex surfaces, especially as regards waves of the second class.
On boundary layers in two-dimensional flow with vorticity
Authors: Harper J. F.
Published: March 2006

The starting-point for this paper is the suggestion (Batchelor 1956b) that the wake behind a bluff body in a uniform stream may consist principally of two eddies rotating in opposite directions. The fluid is assumed to be incompressible and in two-dimensional steady motion at a very high Reynolds number. Along the boundary between the eddies, a viscous layer must form. This layer is unusual in that merely the vorticity, and not the velocity itself, varies appreciably across it. It will be shown that such layers can be treated theoretically much more simply than the general case, because it is possible to linearize the equation of motion. They may, of course, exist in flows other than that past a bluff body.

A discussion is also given of the flow near the rear stagnation point, where this boundary layer meets the body. It had been suggested that a large number of small eddies would have to exist there, but this seems not to be so.
End effects in falling-ball viscometry
Authors: Tanner R. I.
Published: March 2006

A calculation taking into account the interaction of tube wall and ends with a falling sphere is presented, with a view to assessing the change in drag on the sphere due to the end proximity in practical viscometry. It is shown that when the sphere is more than one fall tube radius from the closed end, the extra drag resulting is less than 4·5 × 10−3of the Faxèn drag, and is therefore usually negligible.

For smaller end-sphere distances the end-effect drag increases rapidly, reaching about 1·5 of the Faxèn drag when the sphere centre is 0·25 tube radius from the end. The drag curve lies substantially below that given by Ladenburg (1907). Satisfactory agreement with experiment is found. It is concluded that with the commonly used types of fall tubes, end effects due to a closed end and an open surface will not be detectable.
Torsional oscillations of an infinite plate in second-order fluids
Authors: Srivastava A. C.
Published: March 2006

The flow of an incompressible second-order fluid due to torsional oscillations of an infinite plate when the fluid is infinite in extent as well as the case when it is bounded by another stationary parallel plate has been considered by expanding the velocity components and the pressure in powers of the amplitude of oscillation of the plate. In both cases the first-order solution consists of a transverse velocity and the second-order solution gives a radial-axial flow composed of a steady part and a fluctuating part. In the case of the unbounded plate the steady part of the radial flow does not vanish outside the boundary-layer region. Hence the equations are solved by another approximate method for the steady part of the flow. The effects of the non-Newtonian terms are to increase the non-dimensional boundary thickness and the shearing stress on the plate. In the case of two plates the velocity components and the shearing stresses on the plates have been expressed in powers of Reynolds number R for its small values. Their asymtotic behaviour for large R has also been studied. The asymtotic expansion of the fluctuating part of the radial-axial flow shows that the boundary layer is developed at both the plates.