Flow of a conducting fluid along the annular channel between two non-conducting circular cylinders is examined by a numerical method for concentric and eccentric cases. Solutions have been obtained for Hartmann numbers ranging from 0·1 to 40 and, for some of these, details of velocity distribution and of induced current are given. The results obtained enable the development of the patterns of velocity and of current flow to be traced as the Hartmann number increases. The details of the development of the current flow patterns for eccentric cylinders are particularly interesting and are discussed in detail. At the higher values of Hartmann number studied the solutions are in excellent agreement with the results of Todd's (1967) high Hartmann number analysis and it is possible to determine at what value of Hartmann number Todd's analysis becomes applicable within a specified accuracy. The effect of eccentricity of the cylinders on the flow rate at a fixed pressure gradient is shown to diminish rapidly with increasing Hartmann number. The net flow of current around the annulus, which occurs when the cylinders are eccentric, has a maximum value for each case studied at a Hartmann number of 3, approximately.

The energy of internal waves tends to be propagated along certain characteristic paths inclined at fixed angles to the vertical direction; the angle of inclination depending only on the wave frequency and the density stratification (not on the wavelength). The reflexion of such waves by smooth plane surfaces has been discussed recently by Sandstrom (1966).

In the present paper the role of surface roughness is examined. Surprisingly, it appears that quite small-scale irregularities can completely alter the reflecting properties of a surface; the tangential scale of the roughness elements may be much smaller than the wavelength of the incident or reflected waves. All scales of roughness are relevant, down to those comparable in magnitude to the thickness of the oscillatory boundary layer. For tidal waves in the ocean this thickness is of the order of 1 m.

The behaviour of the coefficient of transmission as a function of the angle of incidence appears at first sight to be extremely complicated. Some simple examples of periodic surface roughnesses are discussed and elucidated: a sawtooth, a square-topped wave and a simple sine-wave. The transmission coefficient T for a sine-wave, for example, is shown in figure 9. An approximate expression for T is also derived in the case of a slowly modulated sine-wave (figure 10). These results are for a non-viscous fluid. The effects of viscosity are also considered qualitatively.

Experiments are performed to demonstrate the occurrence and explore the characteristics of a secondary flow superposed upon the natural convection main flow on an inclined plate. A flow visualization technique is employed whereby the flow pattern is made visible by local changes of colour of the fluid itself, the colour change being brought about by a change in pH. The secondary flow consists of longitudinal vortices or rolls distributed more or less periodically across the width of the plate. The number of such vortices increases with the temperature difference between the surface and the ambient fluid, but appears to be relatively insensitive to the inclination angle of the plate. The secondary flow results from the destabilizing effect of the buoyancy force component, which acts normal to the plate surface. The longitudinal vortices are the first stage of the laminarturbulent transition process. This is in contrast to the case of natural convection on a vertical plate, where the first stage of transition is Tollmien-Schlichting waves.

The steady rise of a given amount of gas in an infinite liquid under the action of buoyancy forces is examined. The shape of the bubble is that of a spherical cap. Behind the bubble there is a region of closed streamlines where the flow is assumed to be steady and rotational. The predicted velocity and geometry of the cap agree well with observation for a limited range of values of the Reynolds number.

Measurements of flow and fluctuating heat transfer were made for a circular cylinder in cross-flow with a transverse standing sound field imposed simultaneously. Reynolds numbers were of the order of 104, known to be in the disturbance-sensitive range, and sound intensities were as large as 140 db. The frequencies of the sound field were of the order of the disturbance frequency in the separated shear layers, reported first by Bloor.

With a sound field having its frequency matched sufficiently closely to that occurring naturally in the shear layer, the growth of the instability is enhanced with the processes of vortex fusion and possibly vortex breakdown being detectable. At the same time, the vortex street frequency is only very weakly affected, although the vortex formation region length is reduced when the instability in the shear layer is enhanced. It is suggested that the discretization of vorticity in the shear layers is one factor significant in reducing the formation length. Heat transfer at the rear of the cylinder fluctuates at frequencies centred on the shedding frequency. The fluctuation level increases as the formation region shortens.

The thermohaline stability problem previously treated by Stern, Walin and Veronis is examined in greater detail. An error in an earlier paper is corrected and some new calculations made. It is shown, for instance, that direct convection can occur for thermal Rayleigh number R much less than 100 Rs when Rs [gsim ] 0·1, where Rs is the salinity Rayleigh number. A graphical presentation is devised to show the relative importance of the different terms in the equations of motion as a function of R and Rs. The most unstable mode over all wave-numbers for each R, Rs is found and it is shown that where both unstable direct and oscillating modes are present, the most unstable mode is direct in most cases.

This paper describes an experiment performed with a fluid-filled sphere whose rotation speed about a fixed axis was forcibly varied in a slight but sinusoidal manner about a non-zero mean value. The object of this experiment was both to excite axisymmetric inertial eigen-oscillations within the relatively low viscosity fluid through the mild pumping action of the oscillatory Ekman boundary layer near the wall, and to measure and compare with theory some of the properties of such modes.

Seven distinct fluid resonances were detected via pressure measurements made along the axis for various ratios of the excitation to the mean rotation frequency. For the three most pronounced of those modes, the observed frequency ratios agree within ½ of 1% with the corresponding ratios predicted from linear, small viscosity theory. The response amplitudes at the various resonances and the rates of decay upon switching off the excitation also compare favourably with theory, although the observed amplitudes are systematically lower and the decays more rapid by a few per cent to several tens of per cent.

The theory referred to above is largely that of Greenspan (1964, 1968). It is in part rederived here from energy considerations.

An experimental investigation of the non-equilibrium behaviour of the shock stand-off distance ahead of spheres at low supersonic Mach number is reported. An intermittent wind tunnel operating with a reacting gas mixture with one non-equilibrium mode is described. A non-equilibrium parameter after Damköhler is determined for the flow and the experiments cover a range of this variable from near-frozen to near-equilibrium states. The shock stand-off distance is measured and found to vary as expected between these two bounds with a low value at equilibrium. With all other variables governing shock standoff distance held constant, such measurements can also be used to determine the relaxation time of the non-equilibrium mode.

A viscous fluid is confined between two parallel, infinite planes which perform torsional oscillations of small amplitude about a common axis. The resulting flow is studied for the case of high-frequency oscillations, when boundary layers form adjacent to moving surfaces. Particular analysis is made of the second-order, steady, radial-axial streaming. It is shown that in certain circumstances viscosity may be effective throughout the domain of flow, while in others there is a region in which viscosity is negligible.

Some recent work on the existence of vibrational de-excitation shocks (δ-shocks) in expanding non-equilibrium nozzle flows is extended to include situations in which an adiabatic shock (δ-shocks) may be embedded within the de-excitation shock. A discussion of some further properties of the shock solution is given and some examples are worked out. Numerical solutions of the full equations are also presented. These solutions confirm the existence of the δ-shocks but bring to light certain anomalies in the simple approximate solution. The modifications necessary to remove these discrepancies are outlined, and the implications of the numerical results are briefly discussed. Finally, some comments on the nature of the asymptotic solution for an arbitrary rate process are made.

The local porosity of a real porous material (obtained by averaging over volumes containing a sufficiently large number of pores) is different from the mean porosity of the material as a whole. This difference is caused by large-scale defects of the porous structure and can be treated as a random function of position in the porous material. Such a random deviation of the local porosity from the average value causes random local flows superimposed upon the mean filtration flow. The characteristic scale of such motion is much larger than that of the flow of a fluid through individual pores. The phenomenon appears to play an important role in transport processes in filtration.

In this paper the statistical characteristics of the random fields under consideration are determined on the basis of the assumption that the local porosity is a random function of position with independent increments. Expressions for correlations of various quantities are obtained in terms of the characteristics of porosity fluctuations and the effective coefficients of diffusion caused by the random motions under study are estimated.

This paper describes a detailed experimental study of turbulent boundary-layer development over rough walls in both zero and adverse pressure gradients. In contrast to previous work on this problem the skin friction was determined by pressure tapping the roughness elements and measuring their form drag.

Two wall roughness geometries were chosen each giving a different law of behaviour; they were selected on the basis of their reported behaviour in pipe flow experiments. One type gives a Clauser type roughness function which depends on a Reynolds number based on the shear velocity and on a length associated with the size of the roughness. The other type of roughness (typified by a smooth wall containing a pattern of narrow cavities) has been tested in pipes and it is shown here that these pipe results indicate that the corresponding roughness function does not depend on roughness scale but depends instead on the pipe diameter. In boundary-layer flow the first type of roughness gives a roughness function identical to pipe flow as given by Clauser and verified by Hama and Perry & Joubert. The emphasis of this work is on the second type of roughness in boundary-layer flow. No external length scale associated with the boundary layer that is analogous to pipe diameter has been found, except perhaps for the zero pressure gradient case. However, it has been found that results for both types of roughness correlate with a Reynolds number based on the wall shear velocity and on the distance below the crests of the elements from where the logarithmic distribution of velocity is measured. One important implication of this is that a zero pressure gradient boundary layer with a cavity type rough wall conforms to Rotta's condition of precise self preserving flow. Some other implications of this are also discussed.