The spiral wind-up and diffusive decay of a passive scalar in circular streamlines is considered. An accelerated diffusion mechanism operates to destroy scalar fluctuations on a time scale of order P^1/3 times the turn-over time, where P is a Péclet number. The mechanism relies on differential rotation, that is, a non-zero gradient of angular velocity. However if the flow is smooth, the gradient of angular velocity necessarily vanishes at the centre of the streamlines, and the time scale becomes greater. The behaviour at the centre is analysed and it is found that scalar there is only destroyed on a time scale of order P^1/2. Related results are obtained for magnetic field and for weak vorticity, a scalar coupled to the stream function of the flow. Some exact solutions are presented.

We examine the effect of local thermal non-equilibrium on the infiltration of a hot fluid into a cold porous medium. The temperature fields of the solid porous matrix and the saturating fluid are governed by separate, but coupled, parabolic equations, forming a system governed by three dimensionless parameters. A scale analysis and numerical simulations are performed to determine the different manners in which the temperature fields evolve in time. These are supplemented by a large-time analysis showing that local thermal equilibrium between the phases is eventually attained. It is found that the thickness of the advancing thermal front is a function of the governing parameters rather than being independent of them. This has the implication that local thermal equilibrium is not equivalent to a single equation formulation of the energy equation as might have been expected. When the velocity of the infiltrating fluid is sufficiently large, the equations reduce to a hyperbolic system and a thermal shock wave is formed within the fluid phase. The strength of the shock decays exponentially with time, but the approach to local thermal equilibrium is slower and is achieved algebraically in time.

The linear stability of the Stokes layer generated by an oscillating flat plate is investigated using Floquet theory. The results obtained include the behaviour of the growth rate of the disturbances, part of the corresponding neutral curve and the structure of neutrally stable disturbances. Previously unknown properties of the growth rate cause the neutral curve to have a complicated geometry: the majority of the marginal curve is defined by waves propagating relative to the basic flow and the curve is smooth in character, but for certain very narrow bands of wavenumbers it was found that stationary modes are the first to become unstable. This phenomenon has the consequence that the underlying smooth neutral curve is punctuated by thin finger-like features. The structure of the eigenfunctions showed that the neutrally stable disturbances tend to grow most rapidly just after the wall velocity passes through zero.