A theoretical and experimental investigation is reported dealing with the onset of buckling in a horizontal layer of highly viscous liquid. The layer floats on a heavier liquid with negligible viscosity, and at rest is stabilized by gravity and surface tension. When sheared at a sufficient rate, the flat configuration of the layer becomes unstable; and the aim of the investigation is to establish the relation between critical values of the shearing rate and values of the layer's thickness and other physical parameters.

A primitive theory based on membrane approximations is first reviewed and its deficiencies are appreciated. Then a more reliable theory is developed, providing estimates of values taken by a dimensionless shear stress f at the threshold of instability. The values fc are found to depend primarily on a dimensionless number H proportional to the thickness of the layer.

Experiments on sheared layers of silicone oil with various high viscosities are then described. Measured values of fc plotted against H over a wide range are shown to be in satisfactory agreement with the theory. Finally, discrepancies between previous experimental results and ours are discussed.

Modelling of turbulent passive-scalar diffusion is studied using the statistical results from a two-scale direct-interaction approximation. In this model, the mean scalar, the scalar variance and the dissipation rate of scalar variance constitute fundamental diffusion quantities. The turbulent scalar flux is written in the form of an anisotropic eddy-diffusivity representation. This representation, paving the way for explaining anisotropic heat transport, is tested against typical experimental data. The present model equation for the dissipation rate of scalar variance also gives a theoretical justification for the existing equations that are adopted in the second-order models.

A cavitating-flow calculation method is presented, based on the panel technique with minimization of a certain vector characterizing the discretion error which may become important under cavitating conditions. Several practical examples are presented: partial cavitation on an isolated foil, cavitation behind a blunt-ended body, and the problem of two cavities around an axisymmetrical body. In the case of partial cavitation, the Joukowski condition and tangential outlet condition can be satisfied by the form of the error vector. The cavity-wake modelling problem is not extensively dealt with. It is shown, however, that in order to obtain a satisfactory cavity length/cavitation number ratio, it is probably necessary to introduce a displacement thickness behind the near wake of the cavity which does not close on the body according to a separated flow scheme analagous to the wake, as introduced previously by Yagamuchi & Kato (1983). The method is shown to be capable, after a few minor modifications, of dealing with the case of bodies with a rounded rear edge. Even so, the advantage is essentially didactic as the problem of predicting the position of separation points is not treated. The problem of two cavities around axisymmetrical bodies has a more obvious practical interest. The nonlinear closure condition of each cavity is exactly satisfied by an iterative resolution scheme in which allowance is made for the presence of an axial gravity field.

A corrugated plate is translating in a rotating fluid. Assuming low Reynolds number and small amplitudes compared to the Ekman thickness, a perturbation solution is found to second order. The resistance and power due to drag depend on the relative orientation of the corrugations with the motion. In certain instances, it is easier to move a corrugated plate than a flat plate in a rotating fluid.

A superposition of δ-function inputs is used to investigate the approach to the steady state, oscillatory discharges, and a Gaussian pulse for high-Péclet-number parallel shear flows. Illustrative results are given for open-channel flow with a logarithmic velocity profile.