By assuming that an uncharged drop situated in a uniform electric field E retains a spheroidal shape while oscillating about its equilibrium configuration, two approximate equations of motion are derived for the deformation ratio γ expressed as the ratio a/b of the major and minor axis of the drop. Solutions of these equations of motion indicate that the stability of a drop of undistorted radius R and surface tension T depends upon E(R/T)½ and the initial displacement of γ from its equilibrium value. The predictions of the two equations are compared to assess the accuracy of the spheroidal assumption as applied to such a dynamical situation. The analysis is used to determine the stability criterion of a drop subject to a step function field. Finally, the limit of validity of the spheroidal assumption is discussed in terms of Rayleigh's criterion for the stability of charged spherical drops. By applying Rayleigh's criterion to the poles of a spheroidal drop, the stage at which the drop departs from spheroidal form to form conical jets was approximately determined.

The factors bringing about the irreversible distortion or degeneration of a continuously forced standing internal gravity wave in a linearly stratified fluid are studied experimentally and theoretically. For a rectangular container there is strong evidence that the process is initiated by the unstable growth, from a subliminal level, of free wave modes forming triads in second-order resonant interaction with the original wave. These free modes grow by de-energizing the original wave and may collectively induce kinematical conditions sufficiently severe to create localized regions of density discontinuity within the fluid, leading to turbulence.

Although the possible free wave modes are doubly infinite in number, the geometrical constraints greatly reduce the number of possibilities for resonant triads. In many cases this permits critical wave amplitude to be predicted by consideration of one triad only, and the results are in excellent agreement with experiment.

It is speculated that a closely similar process explains observations by Malkus (1968), Aldridge & Toomre (1969), and McEwan (1970) in the analogous context of inertial oscillation of contained rotating fluids.

Time-dependent hydromagnetic phenomena in a rotating spherical cavity are investigated in the framework of an interior boundary-layer expansion. The interior problem is shown to contain waves whose frequencies are of order ω, Aω and A2ω, where ω is the rotation rate of the cavity and A2 = B2/4πρωA2 [Lt ] 1 is the Alfvén number. B is an imposed magnetic field, ρ the fluid density and R the radius of the cavity. The first type of wave is a modification of the hydro-dynamic inertial wave, the second is a pseudo-geostrophic wave and is involved in spin-up, and the third is related to the MAC waves of Braginskiy (1967).

It is shown that the MAC waves must satisfy more than the usual normal boundary conditions and that reference must be made to the boundary-layer solution to resolve the ambiguity regarding which conditions are to be taken. For normal liquid metals of small magnetic Prandtl number the MAC waves must satisfy full magnetic boundary conditions; only the no-slip conditions may be deferred to the boundary layers.

The boundary-layer structure is investigated in detail to display the interactions between applied field, viscosity, electrical conductivity, frequency and latitude. The decay of the pseudo-geostrophic modes, essentially the spin-up problem, is discussed for a non-axisymmetric constraining field and non-zero container conductivity. Three regimes exist, depending on container conductivity.

The problems commonly encountered in the measurement of the interfacial tension between two liquids by capillary tube or force measurement are described. In order to avoid such problems, a new method of measurement of the interfacial tension is developed here which is based on the details of axisymmetric capillary waves which can be generated on the interface. Analyses relating these details to the interfacial tension and showing how the details can be measured photographically are given. An apparatus for making these photographic measurements is described and photographs made with such an apparatus are presented. An analysis of these photographs is given which gives the interfacial tensions for the interfaces shown.

A theroetical analysis is given for potential flow over, around and under a vehicle of general shape moving close to a plane ground surface. Solutions are given both in the form of a small-gap asymptotic expansion and a direct numerical computation, with close agreement between the two for two-dimensional flows with and without circulation. Some results for three-dimensional bodies are discussed.

An experimental investigation was performed to study the spatial coherence of structures in the sublayer of a turbulent boundary layer observed previously by flow visualization. The present work verifies these observations in an Eulerian reference frame and develops a statistical description of the phenomenon. The technique involves simultaneous digital sampling of an array of constant temperature hot-wire anemometers arranged to extract information about a spanwise variation in flow quantities. The quantitative description agrees with dimensionless measures of the structure scales previously published.

The autorotation of a flat plate about its spanwise axis was experimentally studied. Most of the work was done with a wing mounted in the University of Michigan 5 × 7 ft low-speed wind tunnel. The measurements consisted of the unsteady lift, drag, angular acceleration and the wing rotation rate. The flow pattern was studied by means of smoke, tufts and a small model in a water tunnel.

The flow pattern was very different from that over a static wing. The wing did not stall until it was nearly perpendicular to the free stream and the flow did not reattach to the lower surface until the wing had rotated well past zero angle of attack.

The maximum and average lift, drag and angular acceleration were measured for Reynolds numbers from 25 000 to 250 000. At Re = 240 000 the maximum lift coefficient was 4·50 with an average value of 2·20, while the maximum drag coefficient was 4·30 with an average value of 1·60. The angular acceleration was small; the wing rotated at an almost constant angular velocity. The non-dimensional wing rotation rate was measured for Reynolds numbers from 1300 to 280 000 and approached an asymptotic limit of 0·35 for sufficiently high Reynolds numbers.

The effect of applying driving and retarding torques to the wing was studied. As the rotation rate was increased above the free autorotation rate, the lift and drag increased. When the rotation rate was reduced by a retarding torque they both decreased. The power developed by the rotating wing was considerably less than for a windmill of the same frontal area.

A variety of wing configurations were tested, including different airfoils and aspect ratios and spoilers mounted at various locations on the wing. However, except for spoilers that were so large that they prevented autorotation, none of these changes had a major effect on the gross properties of the autorotation phenomenon.

Freely falling wings were also studied. For Reynolds numbers above 4000 the average lift and drag coefficients were comparable to those observed in the fixed axis tests and it appeared that the flow pattern was similar.

The novel idea is to use a disk pump to drive each fluid layer independently round a closed-return density-stratified water channel. A small-scale model was built and tested to demonstrate the feasibility of the idea. A hydrogen-bubble technique was used for both flow visualization and velocity measurement. Density measurements were made with an electrical conductivity probe developed by the authors. The tests have demonstrated the usefulness of such a facility, especially for long steady-state experiments in density-stratified flows.

The behaviour of internal gravity waves near a critical level is investigated by means of a transient two dimensional finite difference model. All the important non-linear, viscosity and thermal conduction terms are included, but the rotational terms are omitted and the perturbations are assumed to be incompressible. For Richardson numbers greater than 2·0 the interaction of the incident wave and the mean flow is largely as predicted by the linear theory–very little of the incident wave penetrates through the critical level and almost all of the wave's energy and momentum are absorbed by changes in the original wind. However, these changes in the wind are centred above the critical level, so that the change in the wind has only a small effect on the height of the critical level. For Richardson numbers less than 2·0 and greater than 0·25 a significant fraction of the incident wave is reflected, part of which could have been predicted by the linear theory. For these stable Richardson numbers a steady state is apparently reached where the maximum wind change continues to grow slowly, but the minimum Richardson number and wave magnitudes remain constant. This condition represents a balance between the diffusion outward of the added momentum and the rate at which it is absorbed. For Richardson numbers less than 0·25, over-reflexion, predicted from the linear theory, is observed, but because the system is dynamically unstable no over-reflecting steady state is ever reached.

An analytical study is made of nearly free-molecular flow of a noble gas from one reservoir to another through a two-dimensional slit, with finite pressure and temperature ratios across the slit. The fundamental solution of the linear Boltzmann equation is employed in the study. The total mass flow is calculated to the first-order correction terms, of the order of α ln α and α, where α is the inverse Knudsen number. The coefficients of these terms are in general multiple integrals, but they become explicit functions of the pressure and temperature ratios after the multiple integrations are carried out by using Krook collision model. When the general result is simplified to the isothermal case the first-order correction has a negative value, indicating the reduction of the total mass flow due to intermolecular collisions in the counter flows.

Stratified spin-up, the process of adjustment of a uniformly rotating stratified fluid to an abrupt change in the rotation of the container, is important in many geophysical contexts. An experimental study of this process is presented here for the case where a linearly stratified salt solution is enclosed in a cylindrical container whose rotation rate is changed by a small amount. Results are presented for a limited range of values of B, the internal Froude number, which measures the ratio of the frequencies due to buoyancy and rotation. The experimental study is augmented by a theoretical treatment of idealized models which clarify the more fundamental physical processes that occur. The response of a stratified fluid is faster than that of a homogeneous fluid but the adjustment is limited to layers near the bottom and top boundaries the thickness of which is determined by the value of B. A comparison of the experimental results with the theories of Holton, Walin and Sakurai is also made and it is shown that for the present physical arrangement (insulated side walls) the theories of the latter two authors agree much more closely with experiment than does the theory of Holton. However, all three theories tend to over-estimate the azimuthal displacement in the regions near the upper and lower boundaries where the spin-up is most rapid. The Sweet-Eddington circulation, which accompanies the ideal state of rigid-body rotation, can be significant under normal laboratory conditions and it was necessary to correct some of the spin-up results for this effect. The circulation in the vertical plane is described qualitatively.

The prototype linear spin-up problem consisting of a homogeneous viscous electrically conducting fluid confined between two infinite flat rotating electrically conducting plates in the presence of an applied axial magnetic field is studied in an effort to understand better the strength and nature of the coupling between a fluid and its rotating conducting container. It is assumed that the response time of the bounding plates to a magnetic perturbation is much less than the fluid spin-up time and that the plate conductivity is an arbitrary function of distance from the fluid-plate interface. The general Laplace transform solution is inverted and discussed for three special cases: magnetic diffusion regions thick compared with fluid depth during spin-up, arbitrary magnetic field strength and boundary conductance; magnetic diffusion regions thin, weak conductance, arbitrary field; magnetic diffusion regions thin, strong conductance, arbitrary field. In each case conductance of the boundary strengthens the coupling between fluid and boundary, thereby decreasing the spin-up time. The corresponding single plate analysis of Loper (1970a) is found to predict spin-up accurately only if the boundary conductance is much smaller than that of the fluid. The fluid possesses an oscillatory mode of spin-up if the magnetic diffusion regions are thin and boundary conductance is large. That is, the inviscid current-free core of fluid rotates significantly faster than the boundaries during a portion of the spin-up process.