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

A semi-theoretical study has been made of the problem of stableturbulent heat and mass transfer between a water surface andsurrounding atmosphere under the influence of wind. The equationsderived are based on the principle of similarity and are thereforeexpected to be valid under both laboratory and field conditions. Thepredicted heat- and mass-transfer Stanton numbers appear to be insatisfactory agreement with the available field data.

The singularity at the contact line which is present when the usualfluidmechanical modelling assumptions are made is removed bypermitting the fluid to slip along the wall. The aim of this studyis to assess the sensitivity of the overall flow field to the formof the slip boundary condition. Explicit solutions are obtained forthree different slip boundary conditions. Two length scales emerge:the slip length scale and the meniscus length scale. It is foundthat on the slip length scale the flow fields are quite different;however, when viewed on the meniscus length scale, i.e. the lengthscale on which almost all fluidmechanical measurements are made, allof the flow fields appear the same. It is found that thecharacteristic of the slip boundary condition which affects theoverall flow field is the magnitude of the slip length.

The Wedemeyer model describing the spin-up of a fluid in a rotatingcylinder is generalized to include the case of spin-down. Attentionis focused on spin-up and spin-down at a finite (constant)acceleration for small Ekman numbers En. It is found that when thefull nonlinear Ekman suction is included for spin-up from rest, thecharacteristics near the propagating wave front intersect, thusyielding an O(1) velocity discontinuity for the inviscid model. Thisanomalous behaviour is limited to only a small range of Rossbynumbers and does not appear in any of the spin-down solutions.Transient spin-down velocity profiles in the O(E1/4Ω) shear layer atthe cylindrical wall are calculated for the quasi-steady flow whichoccurs for sufficiently small decelerations. Results for impulsivespin-up and spin-down between infinite parallel plates are presentedand compared with the asymptotic solutions given by Greenspan &Weinbaum and Benton. Finally, characteristic spin-up and spin-downtimes are computed for both the contained cylinder and theinfinite-parallel-plates geometry.

Measurements of the azimuthal velocity inside a cylinder which spinsup or spins down at constant acceleration were obtained with alaser-Doppler velocimeter and compared with the theoretical resultspresented in part 1. Velocity profiles near the wave front inspin-up indicate that the velocity discontinuity given by theinviscid Wedemeyer model is smoothed out in a shear layer whosethickness varies with radius and time but scales with hE1/4Ω. Thespin-down profiles are always in excellent agreement with theorywhen the flow is stable. Visualization studies with aluminiumtracers have made possible the determination of the stabilityboundary for Ekman spiral waves (principally type II waves) observedon the cylinder end walls during spin-up. For spin-down to rest theflow always experienced a centrifugal instability which ultimatelydisrupted the interior fluid motion.

Approximations for shallow-water ship waves are sought which arevalid near the critical speed U = (gh)1/2. For sufficiently thinbodies (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. Asoliton solution is discussed which applies to a sharp-nosedhalf-body at slightly supercritical speed.

Computer simulations of fluid-element trajectories inmirror-symmetric and maximally helical turbulence are used toevaluate Moffatt's (1974) formulae for the magnetic diffusivity η(t)and the coefficient κ(t) of the alpha-effect. The passive-scalardiffusivity κ(t) and the mean response functions of scalar andmagnetic field wave-vector modes are also computed. The velocityfield 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 (frozenturbulence), ω = vo k0 andω0 = 2v0 k0 are followed to t =4/v0 k0. In the ω0 > 0 cases withmaximal helicity, κ(t) and a(t) approach steady-state values oforder vo/k0 and v0, respectively. They behave anomalously forω0 = 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. Thedifference is marked for ω0 = 0. The simulation resultsimply that κ(t) becomes negative in non-normal mirror-symmetricturbulence with strong helicity fluctuations that persist overseveral correlation lengths and times. The computations of responsefunctions 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 growexponentially, and its kurtosis also grows apidly with t, indicatingrapid development of a highly intermittent distribution of magneticfield.

A study has been made of baroclinic instability in a differentiallyheated, rotating fluid annulus whose channel width variesazimuthally. Both laboratory experiments and an a.nalytica1 modelemploying a linear normal-mode analysis have been used. Theexperiments show three types of flow. For slow rotation the flow is'symmetric’, whereas at high rotation speeds baroclinic waves occurat all azimuths. At intermediate rotation speeds it is possible tohave a mixed flow which is ‘symmetric’ in the narrow part but hasbaroclinic waves in the wide part of the annulus. This resultsuggested the analytical investigation of the stability of abarocIinic flow whose meridional scale varies downstream. It wasfound that this model also permits three possible types of flow:everywhere stable, everywhere unstable, and also a mixed flow whichis locally unstable where the meridional scale is largest butlocally stable where the scale is smallest.

The interaction between short internal gravity waves and alarger-scale mean flow in the ocean is analysed in the Wkbjapproximation. The wave field determines the radiation-stress termin the momentum equation of the mean flow and a similar term in thebuoyancy equation. The mean flow affects the propagationcharacteristics of the wave field. This cross-coupling is treated asa small perturbation. When relaxation effects within the wave fieldare considered, the mean flow induces a modulation of the wave fieldwhich is a linear functional of the spatial gradients of the meancurrent velocity. The effect that this modulation itself has on themean flow can be reduced to the addition of diffusion terms to theequations for the mass and momentum balance of the mean flow.However, there is no vertical diffusion of mass and other passiveproperties. The diffusion coefficients depend on the frequencyspectrum and the relaxation time of the internal-wave field and canbe evaluated analytically. The vertical viscosity coefficient isfound to be vv [ape ] 4 x 103cm2/s and exceedsvalues typically used in models of the general circulation by atleast two orders of magnitude.

Conditions leading to the onset of air-flow separation over a mobileair-water interface are discussed. It is argued that, in a frame ofreference in which the interfacial boundary assumes a steady shape,the occurrence of separation requires a stagnation point on theinterface. In the case of air blowing over water waves, thiscorresponds to the onset of wave breaking. These arguments arestrongly supported by flow visualization and pressure measurementscarried out in a laboratory wind-wave flume. Furthermore, thepressure measurements show a greatly enhanced interfacial shearstress for a breaking wave compared with that over an unbroken waveof the same wavelength. The implications of these findings forwind-wave generation are discussed.