The steady motion of a liquid drop in another liquid of comparable density and viscosity is studied theoretically. Both inside and outside the drop, the Reynolds number is taken to be large enough for boundary-layer theory to hold, but small enough for surface tension to keep the drop nearly spherical. Surface-active impurities are assumed absent. We investigate the boundary layers associated with the inviscid first approximation to the flow, which is shown to be Hill's spherical vortex inside, and potential flow outside. The boundary layers are shown to perturb the velocity field only slightly at high Reynolds numbers, and to obey linear equations which are used to find first and second approximations to the drag coefficient and the rate of internal circulation.

Drag coefficients calculated from the theory agree quite well with experimental values for liquids which satisfy the conditions of the theory. There appear to be no experimental results available to test our prediction of the internal circulation.

The fine structure of the summer thermocline in the Mediterranean Sea around Malta, investigated by a new temperature-gradient meter and by photographs of dye tracers, is summarized. The principal internal feature of the thermocline is a series of thin, laminar-flow sheets of high static stability, separated by weakly turbulent layers of only moderate density gradient and a few metres thick. A mechanism for generating the patches of turbulence observed on these thermocline sheets is established by comparing dye photographs with a theory by Miles & Howard (1964).

The formation and growth of three-dimensional wave packets in a laminar boundary layer is treated as a linear problem. The asymptotic form of the disturbed region developing from a point source is obtained in terms of parameters describing two-dimensional instabilities of the flow. It is shown that a wave caustic forms and limits the lateral spread of growing disturbances whenever the Reynolds number is √2 times the critical value. The analysis is applied to the boundary layer on a flat plate and shapes of the wave-envelope are calculated for various Reynolds numbers. These show that all growing disturbances are contained within a wedge-shaped region of approximately 10° semi-angle.

In this paper we examine the stability of a two-dimensional wake profile of the form u(y) = U∞(1 – r e-sy2) with respect to a pulsed disturbance at a point in the fluid. The disturbed flow forms an expanding wave packet which is convected downstream. Far downstream, where asymptotic expansions are valid, the motion at any point in the wave packet is described by a particular three-dimensional wave having complex wave-numbers. In the special case of very unstable flows, where viscosity does not have a significant influence, it is possible to evaluate the three-dimensional eigenvalues in terms of two-dimensional ones using the inviscid form of Squire's transformation. In this way each point in the physical plane can be linked to a particular two-dimensional wave growing in both space and time by simple algebraic expressions which are independent of the mean flow velocity profile. Computed eigenvalues for the wake profile are used in these relations to find the behaviour of the wave packet in the physical plane.

The paper considers the refraction of a plane shock wave at an interface between two streams of different Mach number. Particular attention is paid to the irregular wave systems. It is found that when the interface is slow-fast, that is when the speed of sound a0 in the first or incident wave medium is less than the speed of sound aB in the second or transmitted wave medium, then there are two irregular systems, one being a double Mach reflexion type and the other being a four-wave confluence type. There are also two irregular systems when the refraction is fast-slow; these are a single Mach reflexion type and an expansion wave type. This last system has a central expansion wave when the flow is steady and a continuous band expansion wave when the flow is self-similar. Only two of the irregular wave systems have been observed experimentally in the fully developed state. Possible degeneracies are discussed.

Linear perturbation analysis is applied to the problem of the onset of convection in a horizontal layer of fluid heated uniformly from below, when the fluid is bounded below by a rigid plate of inlinite conductivity and above by a solid layer of finite conductivity and finite thickness. The critical Rayleigh number and wave-number are found for various thickness ratios and thermal conductivity ratios. Both numbers are reduced by the presence of a boundary of finite (rather than infinite) conductivity in qualitative agreement with the observation of Koschmieder (1966).

This paper considers the problem of the stability of an infinite horizontal layer of a viscous fluid which loses heat throughout its volume at a constant rate. The variation of the critical Rayleigh number, Rt, and the cell aspect ratio, a, with the rate of heat loss, is calculated with two sets of boundary conditions corresponding to two free and two rigid boundaries. In both cases we find that, as the rate of heat loss increases, Rt decreases, showing that the layer becomes more unstable, and a increases, showing that the cells become narrower. We also consider the possibility that a double layer of cells is formed for large values of the rate of heat loss, by the stable layer at the top, and find that this does not occur while the temperature of the upper surface of the layer is less than that of the lower.

The wind-driven circulation of a simple model of the oceanic circulation (linear and homogeneous) is investigated in detail to delineate the role of the Ekman layer mass flux in driving hitherto overlooked components of the oceanic circulation.

The role of upwelling boundary-layer regions in driving interior geostrophic circulations is discussed in detail. Several interesting circulations hidden in the earlier transport theories are described.

The spatial distribution of uniformly sized spheres falling in a viscous liquid is investigated experimentally for a solid volume fraction of 0·025 and a single sphere Reynolds number of 0·6. The observed spatial distribution agrees closely with a random distribution based on allocation of spheres to space cells according to a binomial probability mechanism.