In his recent papers, Longuet-Higgins derived a relation of mean angular momentum for gravity waves in deep water. In this paper, an expression for the mean Eulerian angular momentum in water of arbitrary depth is derived. It differs from Longuet-Higgin's expression by an additive term 2IB/g accounting for finite-depth effects, where I is the density of mean horizontal momentum, B the Bernoulli constant and g the gravitational acceleration. In addition, the present derivation appears to be simpler and more straightforward.

This paper describes the consequences of pair interactions in dilute suspensions of rigid rods of length 2l and radius a subjected to weak, steady shear flows. The combination of hydrodynamic and Brownian forces increases alignment with the flow, thereby enhancing the shear thinning and strain thickening expected from dilute theories. The theory is asymptotic in Pe [Lt ] 1 and ε = (ln 2l/a)−1 [Lt ] 1 but requires an ad hoc approximation to simplify the form of the hydrodynamic interactions and the rod-rod excluded volume. The theoretical predictions of the Huggins coefficient in simple shear flow are compared with data in the literature for Xanthan gum, a semi-rigid biopolymer. Comparison with semi-dilute theories emphasizes the fundamentally different nature of the interactions in the two regimes and indicates that the transition between the two lies in the range 1.5 [les ][η]0n [les ] 6.

Creeping flow in two-dimensional periodic channels of arbitrary geometry is considered. The problem is formulated using the boundary-integral method for Stokes flow, presently adapted for periodic flows with special geometrical characteristics. Numerical calculations for steady flow in channels constricted by a plane and a sinusoidal wall are performed. Detailed streamline patterns are presented and criteria for flow reversal are established. It is shown that for narrow channels the mechanism driving the flow has a strong effect on the structure of the flow. The results are discussed with reference to lubrication, coating and molecular-convective processes.

Peristaltic flow in two-dimensional channels with sinusoidal waves is analysed. Under the assumption of creeping motion, the problem is formulated using the boundary integral method for Stokes flow. The effect of channel width, wave amplitude, phase shift, and mean pressure gradient on the streamline pattern and the properties of the flow is considered. The results are discussed with reference to various physiological and engineering processes. It is suggested that under the quasi-steady approximation, peristaltic flow with a varying mean pressure gradient offers an efficient method for molecular-convective transport.

Many different random-walk models of dispersion in inhomogeneous or unsteady turbulence have been proposed and several criteria have emerged to distinguish good models from bad. In this paper the relationships between the various criteria are examined for a very general class of models and it is shown that most of the criteria are equivalent. It is also shown how a model can be designed to satisfy these criteria exactly and to be consistent with inertial-subrange theory. Some examples of models that obey the criteria are described. As an illustration some calculations of dispersion in free-convective conditions are presented.

The linear stability of the ‘ABC’ flows u = (A sinz + C cosy, B sinx + A cosz, C siny + B cosx) is investigated numerically, in the presence of dissipation, for the case where the perturbation has the same 2π-periodicity as the basic flow. Above a critical Reynolds number, the flows are in general found to be unstable, with a growth time that becomes comparable to the dynamical timescale of the flow as the Reynolds number becomes large. The fastest-growing disturbance field is spatially intermittent, and reaches its peak intensity in features which are localized within or at the edge of regions where the undisturbed flow is chaotic, as occurs in the corresponding MHD problem.