The boundary layer on a horizontal cylinder caused by free convection, when the temperature of the cylinder is oscillating harmonically, is considered in a way which is analogous to the problem of a cylinder performing high-frequency oscillations along its diameter. It is found that, outside the thin boundary layer on the cylinder, a steady flow is induced. An outer steady boundary layer, matched with the inner boundary layer, is required in order to be able to satisfy the conditions which apply at large distances from the cylinder.

A strong sound field in a liquid may generate small cavities that move rapidly through the liquid. This paper is an analysis of the equilibrium states, and the conditions for their stability, of a cavity in translational motion through an inviscid, incompressible liquid. A principal conclusion is that translating cavities have a stable size and shape for a wide range of conditions. The equilibrium shape of a stable cavity is approximately an oblate spheroid. It is also found that the presence of translational motion contributes an outward dynamic pressure that tends to enlarge the cavity. As a result, the equilibrium radius of a translating cavity is greater than the equilibrium radius of the same cavity at rest.

A non-linear analysis of cellular convection driven by surface tension in a semi-infinite liquid layer heated from below has been made. The purpose is to determine whether or not one can predict the emergence of the hexagonal flow pattern from the interaction of a certain large class of important disturbances. The principal conclusion is that, compared with gravity driven convection, there is generally a much greater band of imposed temperature difference associated with hexagonal convective patterns. Partial results for the more realistic assumption of finite depth support this conclusion.

The paper deals with the regular refraction of a plane shock at a gas interface for the particular case where the reflected wave is an expansion fan. Numerical results are presented for the air–CH4 and air–CO2 gas combinations which are respectively examples of ‘slow–fast’ and ‘fast–slow’ refractions. It is found that a previously unreported condition exists in which the reflected wave solutions may be multi-valued. The hodograph mapping theory predicts a new type of regular–irregular transition for a refraction in this condition. The continuous expansion wave type of irregular refraction is also examined. The existence of this wave system is found to depend on the flow being self-similar. By contrast the expansion wave becomes centred when the flow becomes steady. Transitions within the ordered set of regular solutions are examined and it is shown that they may be either continuous or discontinuous. The continuous types appear to be associated with fixed boundaries and the discontinuous types with movable boundaries. Finally, a number of almost linear relations between the wave strengths are noted.

In this paper we consider two-dimensional steady cellular motion in a fluid heated from below at large Rayleigh number and Prandtl number of order unity. This is a boundary-layer problem and has been considered by Weinbaum (1964) for the case of rigid boundaries and circular cross-section. Here we consider cells of rectangular cross-section with three sets of velocity boundary conditions: all boundaries free, rigid horizontal boundaries and free vertical boundaries (referred to here as periodic rigid boundary conditions), and all boundaries rigid; the vertical boundaries of the cells are insulated. It is shown that the geometry of the cell cross-section is important, such steady motion being not possible in the case of free boundaries and circular cross-section; also that the dependence of the variables of the problem on the Rayleigh number is determined by the balances in the vertical boundary layers.

We assume only those boundary layers necessary to satisfy the boundary conditions and obtain a Nusselt number dependence $N \sim R^{\frac{1}{3}}$ for free vertical boundaries. For the periodic rigid case, Pillow (1952) has assumed that the buoyancy torque is balanced by the shear stress on the horizontal boundaries; this is equivalent to assuming velocity boundary layers beside the vertical boundaries (rather than the vorticity boundary layers demanded by the boundary conditions) and leads to a Nusselt number dependence N ∼ R¼. If it is assumed that the flow will adjust itself to give the maximum heat flux possible the two models are found to be appropriate for different ranges of the Rayleigh number and there is good agreement with experiment.

An error in the application of Rayleigh's method in this paper is noted and the correct method for carrying the boundary-layer solutions round the corners is given. Estimates of the Nusselt numbers for the various boundary conditions are obtained, and these are compared with the computed results of Fromm (1965). The relevance of the present work to the theory of turbulent convection is discussed and it is suggested that neglect of the momentum convection term, as in the mean field equations, leads to a decrease in the heat flux at very high Rayleigh numbers. A physical argument is given to derive Gill's model for convection in a vertical slot from the Batchelor model, which is appropriate in the present work.

Laboratory and field measurements of the generation of gravity waves by turbulent winds imply that a theoretical model based on laminar flow may be adequate on a laboratory, but not an oceanographic, scale. This suggests that the significance of wave-induced perturbations in the turbulent Reynolds stresses for momentum transfer from wind to waves must increase with an appropriate scale parameter. A generalization of the laminar model is constructed by averaging the linearized equations of motion for a turbulent shear flow in a direction (say y) parallel to the wave crests of a particular Fourier component of the surface-wave field. It is shown that the resulting, mean momentum transfer to this component comprises: (i) a singular part, which is proportional to the product of the velocity-profile curvature and the mean square of the wave-induced vertical velocity in the critical layer, where the mean wind speed is equal to the wave speed; (ii) a vertical integral of the mean product of the vertical velocity and the vorticity ω, where ω is the wave-induced perturbation in the total vorticity along a streamline of the y-averaged motion; (iii) the perturbation in the mean turbulent shear stress at the air-water interface. The equation that governs the advection of the vorticity ω under the action of the perturbations in the turbulent Reynolds stresses is derived. Further theoretical progress appears to demand some ad hoc hypothesis for the specification of these turbulent Reynolds stresses. Two such hypotheses are discussed briefly, but it does not appear worth while, in the absence of more detailed experimental data, to carry out elaborate numerical calculations at this time.

Measurements of the aerodynamic pressure distribution at the interface between air and simple progressive water waves are obtained with the use of a pressure sensor that follows the water surface. The theory of Miles (1957, 1959) and Benjamin (1959) on shear flows past a wavy boundary predicts a phase shift between the pressure distribution along the boundary and the boundary itself. An experimental verification of this theory is sought especially. A wind–wave facility 115 ft. long, 6 ft. high and 3 ft. wide was used. The facility is equipped with an oscil-lating-plate wave-generator which is capable of generating sinusoidal or arbitrary wave-forms, and a suction fan which can produce wind velocities up to 80 ft./sec when the water is at a nominal depth of 3 ft. The pressure sensor used for the measurements of pressure, was mounted on an oscillating device such that the sensor could be maintained at a fixed small distance (within 1/4 in.) above a propagating wavy surface at all times. The perturbation pressure over progressive waves is extracted from recorded data sensed by the moving sensor. The results compare favourably with the theoretical predictions of Miles (1959).

Two interesting linear relations between normal vorticity and current density generated behind a shock wave in three-dimensional unsteady flows of conducting gases have been investigated in order to determine them purely from dynamical considerations. Some interesting physical conclusions have also been made.

This paper indicates the existence of a dual solution of the boundary-layer equations for the flow near a nodal point of attachment of the external flow; especial note is made of the non-axisymmetric boundary-layer flow when the external flow is axisymmetric.

An apparatus is described whereby the distribution of particles in a neutrally buoyant suspension of spheres flowing through a tube may be measured. The discovery of a narrow region of high concentration near to the tube wall, and the behaviour of this ‘wall peak’ at various concentrations and positions along the length of the tube are described. An explanation for this behaviour is put forward in terms of the formation of the peak by interaction of spheres with the tube entrance, and of the formation within this peak of necklace-like strings of particles.

Most of the existing methods for calculating the inviscid flow past a delta wing with leading-edge vortices are based on slender-body theory. When these vortices are represented by rolled-up vortex sheets in an otherwise irrotational flow, some of the assumptions of slender-body theory are violated near the centres of the spirals. The aim of the present report is to describe for the vortex core an alternative method in which only the assumption of a conical velocity field is made. An asymptotic solution valid near the centre of a rolled-up vortex sheet is derived for incompressible flow. Further asymptotic solutions are determined for two-dimensional flow fields with vortex sheets which vary with time in such a manner that the sheets remain similar in shape. A particular two-dimensional flow corresponds to the slender theory approximation for conical sheets.

Experiments giving the mass efflux of a Poiseuille flow over a naturally permeable block are reported. The efflux is greatly enhanced over the value it would have if the block were impermeable, indicating the presence of a boundary layer in the block. The velocity presumably changes across this layer from its (statistically average) Darcy value to some slip value immediately outside the permeable block. A simple theory based on replacing the effect of the boundary layer with a slip velocity proportional to the exterior velocity gradient is proposed and shown to be in reasonable agreement with experimental results.

The drag of spheres and disks has been measured in a flow of liquid sodium within an aligned magnetic field. A slightly viscous, strong field limit is discussed and explored experimentally. In this limit the drag coefficient was found to have an asymptotic dependence proportional to the square root of the interaction parameter, the ratio of magnetic to inertial force, independent of body shape. A physical model is presented along with preliminary verification of its basic characteristics.