A small-scale apparatus was used to examine the effects of surface materials on the initiation of waves on water by the action of wind. Rigorous procedures were followed to ensure freedom from contamination of the initial water surface, and the effect of various forms of subsequent contamination were investigated, using a sensitive moire fringe wave slope observation technique. Provision was made in the design of the water container for insoluble films to circulate, avoiding the downwind buildup of contamination.

In measurements on pure water surfaces, no evidence of a ‘critical wind velocity’ was found, although slightly contaminated water was found to be appreciably less responsive to the wind excitation at wind speeds up to 4 m s−l. Measurements on monolayer-covered surfaces showed that, at these wind speeds, a compressed monolayer of relatively high surface tension and low dilational elasticity can have a greater stilling effect than one of low surface tension and high dilational elasticity. Measurements on a series of solutions of surface-active material, covering a range of surface tensions from 63 to 26 mN m−l at a concentration expected to reduce dilational elasticity by bulk-to-surface diffusion, indicated that the damping effect becomes steadily greater as the surface tension decreases.

Kinematic wave theory is used to determine under what conditions breakdown of a steady or unsteady laminar flow into high frequency oscillations should occur. The analysis of a small-scale secondary wave riding on a large-scale inhomogeneity, such as that produced by a finite amplitude primary instability wave, reveals that the breakdown mechanism has three basic ingredients: (i) a self-excited secondary wave with a group velocity near the propagation velocity (phase velocity) of the primary wave, (ii) space-time focusing of the secondary wave train on the primary wave crest and (iii) a nonlinear filtering mechanism leading to rectification of the secondary wave.

The theory is applied to a laminar shear flow. Good quantitative agreement with the experiments on boundary-layer transition by Klebanoff, Tidstrom & Sargent (1962) is found for the critical condition leading to breakdown. Also, the theory is able to explain all the main qualitative breakdown features observed by Klebanoff et al. and others, such as the rapid localized onset, and the formation of a hairpin vortex lifting up from the surface downstream of the primary wave crest.

An experimental study of asymptotic sink-flow turbulent boundary layers is reported. Three levels of acceleration corresponding to values of the acceleration parameter K of 1·5 × 10−6, 2·5 × 10×6 and 3·0 × 10×6 have been examined. In addition to mean velocity profiles, measurements have been obtained of the profiles of longitudinal turbulence intensity, and, for the lowest value of K, of the lateral and transverse components as well. Measurements at selected positions in the boundary layer of the power spectral density indicate that none of the boundary layers exhibit an inertial subrange; for the steepest acceleration, in particular, throughout the boundary layer the spectrum shapes are similar in form to those reported within the viscous sublayer of a high Reynolds number turbulent flow.

This paper examines the nature of the development of two-dimensional laminar flow of an incompressible fluid at the rear stagnation point on a cylinder which is started impulsively from rest. Proudman & Johnson (1962) first examined this type of flow, andobtainedasimilarity solution of the inviscid form of the equations of motion. This solution describes the nature of the flow at large distances from the surface, for large times after the start of the motion. Here, the flow at the rear stagnation point is examined in greater detail. The solution found by Proudman & Johnson constitutes the leading term in an asymptotic expansion, valid for large times. Further terms in this expansion are now calculated, and the method of matched asymptotic expansions is used to obtain an inner solution describing the flow near the surface. A numerical integration of the full initial-value problem gives good agreement with the analytical solution.

A problem of theoretical interest in suspension rheology is the calculation of bulk rheological properties for a dilute suspension of spherical dipolar particles in the presence of weak Brownian rotation, when the applied field is perpendicular to the local vorticity of the bulk flow. In the present note, we determine the asymptotic form for the orientation distribution of the dipole axis in the limit of weak Brownian motion and use this distribution to determine the corresponding rheological properties of the suspension. The bulk stress is then discussed in terms of an effective viscosity for shear flow.

A layer of fluid containing gradients of both temperature and salinity is subject to several instabilities of geophysical interest. When the salinity and temperature increase upwards, the layer may become unstable even if the density profile indicates stability. This ‘doubly diffusive’ instability, first treated by Stern, is seen experimentally to consist of thin fingers of up- and downgoing fluid. Linear analysis cannot explain this small horizontal scale for a steady-state process, but a nonlinear treatment of the problem combined with a stability analysis indicates that only small-scale motions are stable when the salinity gradient is larger than that necessary for the onset of instability. In the limit of small salt diffusivity the flux of salt is calculated using the Galerkin technique and found to reach a maximum at a wavelength that decreases with increasing salinity and temperature gradients. The stability of the finite amplitude solutions is treated; only small-scale motions are found to be stable and the wavelength of the most stable mode is found to compare favourably with the wavelength that maximizes the salt flux.

An accurate quasi-analytic method of solution is presented for the classical hydrodynamics problem of the constant-velocity entry of a prismatic wedge into a weightless incompressible inviscid fluid. The method uses the Wagner function W, which reduces the problem to the determination of a mapping function Λ = [Lscr ](W) for the hodograph. [Lscr ](W) is constructed by using the hodograph for an unsymmetric diamond together with a modifying or ‘preparatory’ trans-formation. A computer method of conformal mapping is developed and is used to obtain this latter transformation. Results are presented for the case of a 90° wedge and show that the solution is both more accurate than previous solutions, having an error of less than 1 %, and more complete, as it portrays the entire flow field and furnishes information about the functional dependence among the variables.

Two rigid spheres of radii a and b are immersed in infinite fluid whose velocity at infinity is a linear function of position. No external force or couple acts on the spheres, and the effect of inertia forces on the motion of the fluid and the spheres is neglected. The purpose of the paper is to provide a systematic and explicit description of those aspects of the interaction between the two spheres that are relevant in a calculation of the mean stress in a suspension of spherical particles subjected to bulk deformation. The most relevant aspects are the relative velocity of the two sphere centres (V) and the force dipole strengths of the two spheres (S′ij, S″ij), as functions of the vector r separating the two centres.

It is shown that V, S′ij and S″ij depend linearly on the rate of strain at infinity and can be represented in terms of several scalar parameters which are functions of r/a and b/a alone. These scalar functions provide a framework for the expression of the many results previously obtained for particular linear ambient flows or for particular values of r/a or of b/a. Some new results are established for the asymptotic forms of the functions both for r/(a + b) [Gt ] 1 and for values of r − (a + b) small compared with a and b. A reasonably complete numerical description of the interaction of two rigid spheres of equal size is assembled, the main deficiency being accurate values of the scalar functions describing the force dipole strength of a sphere in the intermediate range of sphere separations.

In the case of steady simple shearing motion at infinity, some of the trajectories of one sphere centre relative to another are closed, a fact which has consequences for the rheological problem. These closed forms are described analytically, and also numerically in the case b/a = 1.