The lift tensor for any three-dimensional body moving in a linear shear flow at low Reynolds numbers has been calculated by asympototic methods. The tensor is applied to the problem of the motion of a dumb-bell shaped particle. The particle is shown to have a preferred periodic orbit which corresponds to maximum dissipation. The dissipation is calculated and the intrinsic viscosity of a dilute suspension of such particles is predicted. Experiments conducted with a single particle tend to confirm the stability of the predicted orientation.

The unstrained free turbulent flow generated by a composite grid has been found to possess a distinct, deeply indented boundary separating non-turbulent fluid from turbulent fluid of virtually homogeneous intensity. At this boundary, contraction, in the sense of a reduction in the volume of turbulent fluid, takes place at a rate which is independent not only of the intensity and degree of anisotropy of the turbulence, but also of the relative depth of the surface indentations. The apparent outward spreading of the turbulence is solely due to the increasing amplitude of the boundary bulges.

The subsequent plane straining of the flow in a constant area distortion shows that a reasonably high degree of anisotropy, combined with straining by the mean flow, is required before entrainment of non-turbulent fluid can occur at the boundary. Under these simple straining conditions, the rate of growth of the volume of turbulent fluid appears to be independent of the relative depth of indentations in the turbulence front.

It is considered that in free turbulent shear flows, the potential-turbulent flow boundary will advance into the non-turbulent fluid at a rate which depends on the local mean rate of strain and the local degree of anisotropy adjacent to the front. Contraction is expected to occur on those occasions when the boundary lies in a region of zero mean rate of strain, or when the anisotropy of the turbulence is low. The increased rate of spread due to large eddy activity is thought to be mainly caused by an increase in the probability of the potential-turbulent flow boundary being in a position where the mean rate of strain and local anisotropy are both high, rather than being entirely due to an increase in the surface area of the front.

A second-order theory for equatorial, baroclinic Rossby waves in a bounded ocean yields, among other components, terms of zero frequency. We inquire whether the associated rectified flow (or ‘streaming’, or ‘mass transport’) can be related to the submerged equatorial jet observed by Cromwell, Knauss and others. For quite reasonable models of baroclinic Rossby waves, the resultant streaming can be sharply concentrated at the equator, and varies in depth as N(z), thus giving maximum flow at the thermocline (where the Väisälä frequency N(z) is largest). In this way the rectification hypothesis might account for the observed submerged equatorial steering of the Cromwell current. The observed direction of streaming calls for a predominance of equatorially symmetric Rossby waves. The observed magnitude implies that the r.m.s. fluctuations be of the same order as the mean current; that is to say, we have applied weakinteraction theory to a strong-interaction problem. There are other difficulties.

A non-linear potential problem which describes the injection of a high speed jet into a uniform flow of lower total head is linearized when the jet injection angle is small. The resulting linear problem is solved using the Wiener–Hopf technique. Numerical results for the position of the streamline separating the jet from the free stream and the pressure coefficient along the upstream wall are obtained for various injection angles.

The description of a laminar boundary layer with a constant pressure gradient parameter β but with an initial velocity profile close to that given by the solution of the Falkner-Skan equation for that β, is shown to lead to an eigenvalue problem in much the same manner as prevails for the Blasius solution. However, it is found that only for β > β0, where β0 corresponds to the separation value, and for the upper branch solutions are the eigenvalues all positive and the flow spatially stable. The lower branch solutions involve negative as well as positive eigenvalues and are spatially unstable.

Experiments described here show that the rate of heat transfer in a supersonic, turbulent, boundary layer on a concave wall is increased by the streamwise curvature of the wall. For the arrangement investigated, the pressure is kept constant along the wall, and the increase of about 20% is therefore only due to the wall curvature. For a convex wall, a comparable decrease was found, also with constant pressure along the wall.

It is likely that this change in heat-transfer rate is mainly due to an increase or decrease of turbulent mixing by the effect of the curvature. The increase on a concave wall can in principle also be explained by large-scale vortices with axes in the flow direction (Görtler vortices). However, disturbances of this type cannot explain the decrease observed on the convex wall. They cannot therefore be the only cause.

A simple criterion indicating the effect of curvature on the turbulent motion normal to the wall is given. It is derived from an inviscid-flow analysis. The criterion shows that, for most Mach numbers and wall temperatures of practical interest, the change in mixing depends mainly on the velocity gradient normal to the wall. For high supersonic and hypersonic Mach numbers, however, there is a layer near the outer edge of the boundary layer where the change depends mainly on the temperature (density) gradient.

The steady two-dimensional flow of an inviscid incompressible fluid of variable density is considered in a long channel, bounded above by a rigid horizontal plane and below by an obstacle. For certain variations with height of the speed aud density in the incident stream, the governing equation is the reduced wave equation. Drazin & Moore (1967) have recently used this fact to develop a waveguide analogy. In this note the wave-guide analogy is further developed and several uniqueness theorems obtained. When the obstacle satisfies a certain convexity condition it is shown that the upstream conditions and the obstacle uniquely determine the flow; that is, there is no critical internal Froude number or obstacle height for which the problem fails to be well posed.

This paper shows how electrochemical techniques can be used in studies of flow around solid objects to measure the velocity gradient at the solid boundary. The method holds the advantages that it is not necessary to calibrate and that the test element is easy to fabricate. A study of the distribution of the wall velocity gradient around a cylinder of 1 in. diameter indicates that boundary-layer theory correctly predicts the measurements between the front stagnation point and the separation for Reynolds number, R, greater than 150. The wall velocity gradients in the wake are much smaller than in the front part of the cylinder and they reveal a minimum which is quite close to the separation point.

An investigation is made of the stability of time-periodic azimuthal flows between coaxial, circular cylinders. The disturbance equations are linearized and consideration is limited to the effects of axisymmetric disturbances in a fluid with zero viscosity. It is found convenient to examine separately the cases of flows with zero time-mean and non-zero time-mean respectively. Some remarks are made concerning the definition of stability in relation to such flows and their general stability characteristics are evaluated and discussed.

Hydromagnetic surface waves propagating on the surface of a finitely conducting fluid are studied experimentally and theoretically. An alternating magnetic field is used, so that the field is largely excluded from the bulk of the fluid. Thus, the magnetic damping of the waves is negligible, and the perfectly conducting d.c. case is simulated. The effects of a finite electromagnetic skin depth, δ, are included in the calculation of the theoretical wave dispersion relation. It is predicted that as δ is increased and becomes comparable to the wavelength of the surface wave, the effect of the magnetic field on the fluid motion is decreased. This prediction is confirmed experimentally.

Chandrasekhar's (1961) solution to the eigenvalue equation arising from the Kelvin-Helmholtz stability problem for a rotating fluid is shown to be incorrect. The unstable modes are correctly enumerated with the aid of Cauchy's principle of the argument. Various previously published solutions using Chandrasekhar's analysis are corrected and extended.

An analysis of the structure of the wakes and waves in steady compressible magnetohydrodynamics is presented. No restriction is made on the equation of state of the gas or on the ratios of the various dissipative parameters. An asymptotic solution is obtained which furnishes directly the flow far from a body and which may be used in the construction of the entire flow field. The non-dissipative solutions are obtained as a non-uniform limit for vanishing dissipation; no matter how small the dissipation, one can go far enough from the origin that the flow is essentially dissipative. For non-aligned fields the wave pattern consists of a downstream wake and either two or four standing waves, depending on the flow regime. For aligned fields, two of these waves become wakes, so that the wake is a superposition of three structured layers, with either all downstream or two downstream and one up-stream. It is found that the non-dissipative limit of the wake is non-unique for the aligned fields case. Different limits are obtained depending on how the various dissipative parameters vanish.

An analysis of the mixing of a turbulent half-jet along a curved streamline is presented. Equations of motion referred to streamline co-ordinates are simplified by boundary-layer approximations and integrated under the assumption of similarity. A curved potential flow is dissipated by turbulence in the mixing region, resulting in a maximum value in the velocity distribution across the stream for convex flows, while the distribution is monotonic for concave flows. Pressure distributions across the stream are also presented.

An experimental study of the effects of large longitudinal magnetic fields on the pipe flow of mercury has been made. The experiments were designed to provide large magnetic interaction parameters and thereby to have an important effect upon transition from laminar to turbulent flow and upon the structure of any turbulence. The friction factor and the transition Reynolds number were measured as functions of the magnetic field strength. The friction factor was obtained from accurate measurement of the pressure gradient along the tube. The transition Reynolds number was determined from measurements of the intermittency factor obtained using a hot-wire anemometer.

The results indicate that all relevant stability theories vastly over-estimate the stabilizing effect of the field. The results also indicate that viscosity plays a critical role in delaying transition and in reducing the friction factor of fully developed flows. This, in turn, leads to the important conclusion that the magnetic field has an important effect on the generation of new turbulence, as well as upon the damping of already generated turbulence.