The rate of longitudinal dispersion of a contaminant in a current depends upon concentration variations across the flow. These variations are generated by the combination of a longitudinal concentration gradient and a cross-stream velocity shear. However, the response is not instantaneous and so not only is the dispersion coefficient D(τ) time-dependent, but also there is a memory of the concentration distribution at earlier times. In this paper it is shown that these features are accurately reproduced by the delay-diffusion equation \[ \partial_t\bar{c} \overline{u}\partial_x\bar{c} - \overline{\kappa}\partial^2_x\bar{c} - \int_{0}^{\infty}\partial_{\tau} D\partial^2_x\bar{c}\left(x-\int_0^{\tau}\tilde{u}(\tau^{\prime})\,d\tau^{\prime},t-\tau\right)\,d\tau = \bar{q}(x, t), \] where $\bar{q}$ is the source strength, $\bar{u}$ the bulk velocity and $\tilde{u}$ a transport velocity for the free decay of cross-stream concentration variations.

The purpose of the study was to examine the influence of a nearby wall on the lift experienced by spheres fixed in a fluid stream, and the decay of this influence with increasing separation from the wall. For gaps less than one quarter of the sphere diameter, wall effects were found to dominate all dependencies other than that on Reynolds number. At larger gap ratios the lift vector rotates around the flow axis, sometimes this way and sometimes that but only occasionally changes direction abruptly. The rotation seems to be associated with free-stream turbulence and is inhibited by shear or by uneven surface roughness. These effects are not influenced by sphere mounting, and sphere rotation does not seem important.

Three series of experiments are described, each using different apparatus. In a Reynolds number range 3000–50000, calculated from sphere diameter and relative local velocity, repeatable lift values were observed in zones close to a flow boundary (the wind-tunnel wall), and remote from a boundary for smooth spheres. For rough spheres, results were erratic remote from the boundary.

Large persistent lift forces away from the boundary were found when the gap was less than 0·02 diameters and when it lay between 0·1 and 0·2 diameters (all these fractions being approximate). For larger gaps the lift force was strongly time-dependent and time-averaged values were smaller than those for gap ratios less than 0·2.

Lift forces are related to localized downstream displacements of the separation line round the sphere whose origin seems to lie in the response of the sphere's boundary layer to turbulent structures in the free stream. Weak regularities of the lift record are related not only to the incidence of such features but also to a natural time-scale of response of the boundary layer. Separation line disturbances do not propagate in a predictable fashion but do develop sharp boundaries as a result of recirculation in the wake.

In one series of experiments considerable pains were taken to allow the sphere to rotate freely about an axis parallel to the local tunnel wall and normal to the flow direction. No significant rotation occurred and the effects reported are not associated with sphere rotation. In shear flow remote from a boundary mean lift acted down the gradient of relative velocity.

Steady convective motions in a Boussinesq fluid with an unstable thermal and stable salinity stratification are investigated in the case that the ratio of diffusivities τ = κS/κT [Lt ] 1. Using perturbation theory, it is shown that, for any value of the salt Rayleigh number RS, finite-amplitude convection can occur at values of the Ray-leigh number RT much less than that necessary for infinitesimal oscillations, provided only that T is sufficiently small. A simple qualitative argument is used to show how Rmin, the minimum value of RT for steady convection, varies with RS, and it is shown that the analytical results of the present paper form a natural complement to the numerical ones of Huppert & Moore (1976). Results are presented both for stress-free and for rigid boundaries, and applicability of the method to other related problems is suggested.

The centrifugal instability of a Stokes layer has been investigated by Seminara & Hall (1976, 1977). It was found that the Stokes layer on a torsionally oscillating circular cylinder is unstable to perturbations periodic along the axis of the cylinder when the Taylor number for the flow exceeds a certain critical value. The weakly nonlinear theory given by Seminara & Hall showed that, if nonlinear effects are considered, at this Taylor number a stable axially periodic equilibrium flow bifurcates from the basic circumferential flow. It is known experimentally that this equilibrium flow becomes unstable to disturbances having a longer axial wavelength at a second critical Taylor number about 10% greater than the first critical value. Moreover it is known that, in the initial stages of this destabilization, a mode having twice the axial wavelength of the fundamental is present. In this paper we investigate the linear stability of the bifurcating solution to such a subharmonic mode. An approximate solution of the linear stability problem shows that the subharmonic becomes unstable at a Taylor number remarkably close to the experimentally measured second critical Taylor number.