An analysis is presented of the flow field near a neutrally-buoyant rigid spherical particle immersed in an in compressible Newtonian fluid which, at large distances from the particle, is undergoing simple shear flow. Subject to conditions of continuity of stress at the particle surface and to conditions of zero net torque and zero net force on the sphere, the effect of fluid inertia on the velocity and pressure fields in the vicinity of the particle has been computed to $O(R^{\frac{3}{2}})$, where R = a2G/ν is a shear Reynolds number, a being the sphere radius, G the velocity gradient in the free stream (taken to be a positive number), and ν the kinematic viscosity.

Some streamlines have been computed and plotted. These illustrate how the fore–aft symmetry of the creeping-motion solution is destroyed when one includes inertial effects.

Knowledge of the velocity and pressure fields enables one to compute the effect of inertial forces in suspension rheology. The results include a correction to the Einstein viscosity law to $O(R^{\frac{3}{2}})$ for a dilute (non-interacting) suspension of spheres. In addition it is found that inertial effects give rise to a non-isotropic normal stress.

A derivation is given of the Eulerian equations of motion directly from the Lagrangian formulation of Hamilton's principle. The circulation round a circuit of material particles of uniform entropy appears as a constant of the motion associated with the indistinguishability of fluid elements with equal density, entropy and velocity. A discussion is given of the Lin constraint, and it is pointed out that, for a barotropic fluid, the variational principle recently suggested by Seliger & Whitham does not permit velocity fields in which the vortex lines are knotted.

Observations were made of the appearance of hydrodynamic cavities behind a series of axisymmetric headforms. Among the phenomena investigated was the transition of the interfacial or separated boundary layer on the cavity surface. The first stage of this process, namely the spatial growth of instability waves could be distinguished by means of high-speed photography. Comparison is made with a theoretical instability analysis.

Experiments on fully developed cavity flows were carried out with the prime initial objective of investigating the effects of the addition of small quantities of ‘turbulent drag reducing additive’ upon the cavity-surface boundary-layer instability and transition reported in the previous paper (Brennen 1970). However, in most instances, the additives were found to cause an unforeseen instability in the wetted surface flow around the headform. Upon convection, the resulting disturbances dramatically disfigured the cavity surface, thus negating the original purpose. This new phenomenon warranted investigation and became the principal subject of this paper.

A constitutive equation for dilute emulsions is developed by considering the deformations, assumed infinitesimal, of a small droplet freely suspended in a time-dependent shearing flow. This equation is non-linear in the kinematic variables and gives rise to ‘fluid memory’ effects attributable to the droplet surface dynamics. Furthermore, it has the same form as the corresponding expression for a dilute suspension of Hookean elastic spheres (Goddard & Miller 1967), and reduces to a relation previously proposed by Schowalter, Chaffey & Brenner (1968) when time-dependent effects become small.

Numerical solutions are also presented for the case of a small bubble in a steady extensional flow for the purpose of estimating the range of validity of the small deformation analysis. It is shown that, unlike the drag of a bubble which, in creeping motion, is known to be relatively insensitive to its exact shape, the macroscopic stress field in an emulsion is not well described by the present analysis unless the shapes of the deformed bubbles agree closely with those given by the first-order theory. Thus, the present rheological equation should prove of value in a qualitative rather than a quantitative sense.

In a laboratory study, the class of instabilities of the laminar Ekman layer called type II (or class A) are found to have the spectral characteristics of narrow-band noise (Q ∼ 5). The unperturbed laminar profile resembles very closely the ideal Ekman solution. The frequency of the spectral peak varies with the Reynolds number as predicted theoretically by Lilly (1966), but the measured frequencies are only 60% of the predicted value. The critical Reynolds number for this instability is found to be 56·7, in good agreement with Lilly's analysis. The measured boundary layer profile of the magnitude of the spectral peak has the behaviour predicted by Lilly. A sudden onset of turbulence is found at a Reynolds number of 148.

Observations are reported on the growth of vortices in the vortex sheets bounding the jet emerging from a sharp-edged two-dimensional slit and from a sharp-edged circular orifice. A regular periodic flow is observed near the orifice for both configurations when the Reynolds number of the jet lies between about 500 and 3000. The two-dimensional jet produces a symmetric pattern of vortex pairs with a Strouhal number of 0·43. Vortex rings are formed in the circular jet with a Strouhal number of 0·63. Computer experiments show that a growing pair of vortices in two parallel vortex sheets produces a symmetric pattern of vortices upstream from the original disturbance.

Kennett (1963) calculated the hypersonic flow fields past the lower (compression) surface of a delta wing, using the one-strip approximation of the method of integral relations. He obtained solutions only for wings with detached shocks. In this paper, his solutions are extended to wings with attached shocks. Here, the sonic point is inboard of the leading edge which makes the problem mixed. The solutions compare very well with the numerical solutions of the full equations by Babaev (1963a) both in the shock shapes and pressure distributions for various Mach numbers.

Significant experimental results from a study of pressure in the water-entry cavity are presented. Projectiles were fired into water at velocities up to 250 ft./sec and entry angles of 90°, 60°, and 45°. Pressure data obtained using underwater probes were correlated with high-speed motion pictures taken of the entries. Results indicate that the cavity pressure drop prior to surface closure is an order of magnitude greater than previously assumed. As the entry angle is decreased from 90°, the pressure drop decreases. The minimum cavity pressure decreases linearly with increasing entry velocity over the test range. As the entry angle is increased, the minimum entry velocity required to produce a measurable pressure drop becomes greater. An improved pressure-volume correlation is obtained if the volume enclosed by the cavity walls is corrected to account for re-entrant jet volume and air volume enclosed by the splash walls. Cavity pressure during the closed cavity phase behaves approximately according to the isentropic pressure–volume relation. Pressure drop and history are strongly dependent on projectile nose geometry. No appreciable cavity pressure gradient, axial or transverse, was found to exist. Deep closure or cavity collapse is accompanied by relatively high-pressure pulses.

Structure functions of turbulent velocity fluctuations up to fourth order have been measured at several heights in the atmospheric boundary layer over the open ocean, and the results are compared with theoretical predictions for separations in the inertial subrange. The behaviour of second- and third-order quantities shows substantial agreement with the predictions of Kolmogorov's original theory over a wide range of separations, but the results of a recent modification of the theory, attempting to account for intermittency in the local dissipation rate, are also consistent with the data over somewhat shorter separation intervals. The behaviour of the measured fourth-order structure function disagrees with that predicted from Kolmogorov's original work, but good agreement is found with the results of the modified theory.

A three-dimensional barotropic model of the wind-driven ocean circulation is examined and the flow near the east coast of the ocean is considered in detail. The model is linear and has constant coefficients of eddy viscosity. It is shown that a strong current may exist in the eastern boundary layer when upwelling or downwelling is present. No net northwards transport is produced as an equal deep counter current also occurs. A consequence of the downwelling is that the principal interior gyre is prevented from reaching the east coast and a secondary gyre is formed in this region.

Measurements were made of some of the properties of grid-generated, turbulence for several concentrations of a drag-reducing polymer additive in water. Reference measurements of the grid pressure drops, streamwise intensities and one-dimensional spectra in pure water agreed with previous measurements obtained in Newtonian fluids. Corresponding results for the polymer solutions showed that the grid pressure drops were generally lowered, the turbulence intensity levels were increased and the one-dimensional energy spectra were unchanged compared to the results in water. A dimensionless rate of decay correlation was introduced which removed the dependence of the rate of decay on the initial conditions of grid-generated turbulence for Newtonian fluids: the polymer solution decay results did not follow this correlation, indicating that the decay process is different in these fluids. The one-dimensional energy spectra of the turbulence in the polymer solutions were of the same shape as those in Newtonian fluids, and were normalized with modified Kolmogoroff variables using an effective viscosity (Lumley 1964) and the viscous dissipation in order to provide a quantitative comparison to Newtonian spectra. All of the normalized spectra in the polymer solutions collapsed to a single curve which coincided with the normalized Newtonian spectral curve. It was also found that the rate of decay was less than the viscous dissipation in the polymer solutions, in accordance with recent theoretical predictions.

The breakdown of shallow water waves into forms exhibiting several secondary crests is analyzed by numerical computations based on approximate equations accounting for the effects of non-linearity and dispersion. From detailed results of two cases it is shown that when long waves are such that the parameter σ = ν*L*2/h*3 is of moderate magnitude, either due to initially steep waves generated at a wave-maker or due to forced amplification by decreasing depth, waves periodic in time do not remain simply periodic in space. Numerical results are compared with experiments for waves propagating past a slope and onto a shelf.