In this paper, it is shown that if two spheres of equal radii are placed axisymmetrically in a steady Stokes stream, separation of the flow from the spheres occurs if the distance between their centres is less than approximately 3-67 times the sphere radius. For spheres whose spacing is less than this value, wakes form on both spheres and the fluid within the wakes moves in closed eddy type motion. When the distance between the centres of the spheres is less than approximately 3.22 times the sphere radius, a cylinder of fluid links both spheres, and within this cylinder the fluid rotates in one or more ring vortices, the number of vortices increasing as the distance between the spheres is decreased. When the spheres are in contact, the fluid rotates in an infinite set of nested ring vortices.

A semi-theoretical study has been made of the problem of stable turbulent heat and mass transfer between a water surface and surrounding atmosphere under the influence of wind. The equations derived are based on the principle of similarity and are therefore expected to be valid under both laboratory and field conditions. The predicted heat- and mass-transfer Stanton numbers appear to be in satisfactory agreement with the available field data.

The singularity at the contact line which is present when the usual fluidmechanical modelling assumptions are made is removed by permitting the fluid to slip along the wall. The aim of this study is to assess the sensitivity of the overall flow field to the form of the slip boundary condition. Explicit solutions are obtained for three different slip boundary conditions. Two length scales emerge: the slip length scale and the meniscus length scale. It is found that on the slip length scale the flow fields are quite different; however, when viewed on the meniscus length scale, i.e. the length scale on which almost all fluidmechanical measurements are made, all of the flow fields appear the same. It is found that the characteristic of the slip boundary condition which affects the overall flow field is the magnitude of the slip length.

The Wedemeyer model describing the spin-up of a fluid in a rotating cylinder is generalized to include the case of spin-down. Attention is focused on spin-up and spin-down at a finite (constant) acceleration for small Ekman numbers En. It is found that when the full nonlinear Ekman suction is included for spin-up from rest, the characteristics near the propagating wave front intersect, thus yielding an O(1) velocity discontinuity for the inviscid model. This anomalous behaviour is limited to only a small range of Rossby numbers and does not appear in any of the spin-down solutions. Transient spin-down velocity profiles in the O(E1/4Ω) shear layer at the cylindrical wall are calculated for the quasi-steady flow which occurs for sufficiently small decelerations. Results for impulsive spin-up and spin-down between infinite parallel plates are presented and compared with the asymptotic solutions given by Greenspan & Weinbaum and Benton. Finally, characteristic spin-up and spin-down times are computed for both the contained cylinder and the infinite-parallel-plates geometry.

Measurements of the azimuthal velocity inside a cylinder which spins up or spins down at constant acceleration were obtained with a laser-Doppler velocimeter and compared with the theoretical results presented in part 1. Velocity profiles near the wave front in spin-up indicate that the velocity discontinuity given by the inviscid Wedemeyer model is smoothed out in a shear layer whose thickness varies with radius and time but scales with hE1/4Ω. The spin-down profiles are always in excellent agreement with theory when the flow is stable. Visualization studies with aluminium tracers have made possible the determination of the stability boundary for Ekman spiral waves (principally type II waves) observed on the cylinder end walls during spin-up. For spin-down to rest the flow always experienced a centrifugal instability which ultimately disrupted the interior fluid motion.

Approximations for shallow-water ship waves are sought which are valid near the critical speed U = (gh)1/2. For sufficiently thin bodies (struts or ships) the governing equation is dispersive. Simple analytic solutions are given which are valid for all F2 ≤ O(1). As the thickness increases, nonlinearity also enters. A soliton solution is discussed which applies to a sharp-nosed half-body at slightly supercritical speed.

Computer simulations of fluid-element trajectories in mirror-symmetric and maximally helical turbulence are used to evaluate Moffatt's (1974) formulae for the magnetic diffusivity η(t) and the coefficient κ(t) of the alpha-effect. The passive-scalar diffusivity κ(t) and the mean response functions of scalar and magnetic field wave-vector modes are also computed. The velocity field is normal, stationary, homogeneous and isotropic with spectrum $E(k) = \frac{3}{2}v^2_0\delta(k - k_0)$ and time correlation exp [−1/2ω2/0(t-t)2]. The cases ω0 = O (frozen turbulence), ω = vo k0 and ω0 = 2v0 k0 are followed to t = 4/v0 k0. In the ω0 > 0 cases with maximal helicity, κ(t) and a(t) approach steady-state values of order vo/k0 and v0, respectively. They behave anomalously for ω0 = 0. In the mirror-symmetric: cases, q(t) and κ(t) differ very little from each other. At all the ω0 values, is bigger in the helical than in the mirror-symmetric case. The difference is marked for ω0 = 0. The simulation results imply that κ(t) becomes negative in non-normal mirror-symmetric turbulence with strong helicity fluctuations that persist over several correlation lengths and times. The computations of response functions indicate that asymptotic expressions for these functions, valid for k [Lt ]; k0, retain good accuracy for k ∼ k0. The mean-square magnetic field is found to grow exponentially, and its kurtosis also grows apidly with t, indicating rapid development of a highly intermittent distribution of magnetic field.

A study has been made of baroclinic instability in a differentially heated, rotating fluid annulus whose channel width varies azimuthally. Both laboratory experiments and an a.nalytica1 model employing a linear normal-mode analysis have been used. The experiments show three types of flow. For slow rotation the flow is 'symmetric’, whereas at high rotation speeds baroclinic waves occur at all azimuths. At intermediate rotation speeds it is possible to have a mixed flow which is ‘symmetric’ in the narrow part but has baroclinic waves in the wide part of the annulus. This result suggested the analytical investigation of the stability of a barocIinic flow whose meridional scale varies downstream. It was found that this model also permits three possible types of flow: everywhere stable, everywhere unstable, and also a mixed flow which is locally unstable where the meridional scale is largest but locally stable where the scale is smallest.

The interaction between short internal gravity waves and a larger-scale mean flow in the ocean is analysed in the Wkbj approximation. The wave field determines the radiation-stress term in the momentum equation of the mean flow and a similar term in the buoyancy equation. The mean flow affects the propagation characteristics of the wave field. This cross-coupling is treated as a small perturbation. When relaxation effects within the wave field are considered, the mean flow induces a modulation of the wave field which is a linear functional of the spatial gradients of the mean current velocity. The effect that this modulation itself has on the mean flow can be reduced to the addition of diffusion terms to the equations for the mass and momentum balance of the mean flow. However, there is no vertical diffusion of mass and other passive properties. The diffusion coefficients depend on the frequency spectrum and the relaxation time of the internal-wave field and can be evaluated analytically. The vertical viscosity coefficient is found to be vv [ape ] 4 x 103cm2/s and exceeds values typically used in models of the general circulation by at least two orders of magnitude.

Conditions leading to the onset of air-flow separation over a mobile air-water interface are discussed. It is argued that, in a frame of reference in which the interfacial boundary assumes a steady shape, the occurrence of separation requires a stagnation point on the interface. In the case of air blowing over water waves, this corresponds to the onset of wave breaking. These arguments are strongly supported by flow visualization and pressure measurements carried out in a laboratory wind-wave flume. Furthermore, the pressure measurements show a greatly enhanced interfacial shear stress for a breaking wave compared with that over an unbroken wave of the same wavelength. The implications of these findings for wind-wave generation are discussed.