The effects of bottom friction on coastal trapped waves were investigated using an f-plane, two-layer model including shelf-slope topography. At a change-over latitude where the phase speeds of the internal Kelvin wave and the continental-shelf wave coincide, there are two types of behaviour of the ‘frictional’ eigenvalue (the phase speed and the damping rate) and the eigenfunctions, in terms of the inertial frequency f: if the frequency ω is large, wave characteristics change from one wave to another with f (Case II); while if ω is small enough, the wave characteristics do not change (Case II). In actual environments, it is predicted that the weather-band phenomena (period 2 days to 2 weeks) correspond to Case I, and very low-frequency (VLF) phenomena such as signals of El Niño along the American Continent correspond to Case II. Further, for baroclinic VLF waves, it is found that bottom friction retards the lower-layer velocity, which causes a decrease in damping. Therefore, the VLF signals caused by El Niño can travel far from their origin, overcoming the effect of bottom friction. A bottom-intensified structure in barotropic VLF waves, due to bottom friction, has also been found.

Two-dimensional motions generated by Langmuir circulation instability of stratified layers of water of finite depth are studied under a simplifying assumption making it mathematically analogous to double-diffusive thermosolutal convection with constant solute concentration and constant heat flux at the boundaries. The nature of possible motions is mapped over a significant region in (S, R) parameter space, where S and R are parameters measuring, respectively, the stabilizing and destabilizing agencies in the problem. In the Langmuir circulation problem R measures the effects of wind and surface wave action, and S measures the stabilizing effect of buoyancy: in the thermosolutal problem, R measures the destabilizing effects of heating, while S measures the stabilizing effect of solute concentration. Effects of lateral boundary or symmetry conditions are found to be crucial in determining the qualitative behaviour. Complex temporal behaviour, including intermittently chaotic flows, are found under suitably constrained (no flux) lateral conditions but are unstable and not realized when these constraints are relaxed and replaced by periodic lateral conditions. Multiple steady states also arise, with those found under constrained lateral conditions losing stability either to travelling waves, or to other steady states when the lateral boundary conditions are relaxed. In some regions of the parameter space, multiple stable nonlinear motions have been found under periodic boundary conditions. The multiple stable states may either be coexisting travelling waves and steady states (different from those found under the constrained lateral conditions). The existence of robust travelling waves may explain some field observations of laterally drifting windrows associated with Langmuir circulations.

The stability of the buoyancy-driven parallel shear flow of a variable-viscosity Newtonian fluid between vertical or inclined plates maintained at different temperatures is studied theoretically. The analysis is capable of dealing with arbitrary viscosity-temperature relations. Depending on the Prandtl number, angle of inclination, and form of the viscosity-temperature variation, the flow may become unstable with respect to two-dimensional longitudinal or transverse disturbances. Outstanding questions arising in previous investigations of the stability of parallel free-convection flows of constant-viscosity fluids in inclined slots and of variable-viscosity fluids in vertical slots are discussed. We find that, in a variable-viscosity fluid, non-monotonic dependence of the critical Rayleigh number on the inclination angle can occur at significantly higher Prandtl numbers than is possible in the constant-viscosity case. Results are also presented for the stability of the free-convection flow of several glycerol-water solutions in an inclined slot.

Plane stagnation-point flow is modulated in the free stream so that the velocity components are proportional to KH + K cosωt. Similarity solutions of the Navier-Stokes equations are examined using high-frequency asymptotics for K and KH of unit order. Special attention is focused on the steady streaming generated in this flow with strongly non-parallel streamlines. For small modulation amplitude K [les ] KH, unique self-similar streaming flows exist. For large modulation amplitude K > KH, if (K/ω) (K/KH) [ges ] 1.661 no self-similar streaming is possible, while if 4/3 [les ] (K/ω) (K/KH) [les ] 1.661, then multiple steady solutions occur.

The problem of swimming at low Reynolds number is formulated in terms of a gauge field on the space of shapes. Effective methods for computing this field, by solving a linear boundary-value problem, are described. We employ conformal-mapping techniques to calculate swimming motions for cylinders with a variety of crosssections. We also determine the net translationl motion due to arbitrary infinitesimal deformations of a sphere.

We study the effeciencies of swimming motions due to small deformations of spherical and cylindrical bodies at low Reynolds number. A notion of efficiency is defined and used to determine optimal swimming strokes. These strkes are composed of propagating waves, symmetric about the axis of propulsion.