The nonlinearity of the gravity sea flow past a three-dimensional flat blunt ship with a length-based Froude number of order unity is studied using the method of matched asymptotic expansions. It is shown that the nonlinearity is important in an inner domain near the ship, whereas the flow in the rest of the fluid domain is the solution of a Neumann-Kelvin problem. Two possible inner solutions – a jet and a wave – are obtained and discussed.

Quadrant analysis has been used to investigate the events contributing to the Reynolds shear stress in zero-pressure-gradient turbulent boundary layers over regularly arrayed rough surfaces of several different densities, and over a smooth surface. By partitioning the stress into ejections, sweeps, and inward and outward interactions, it is shown that sweeps account for most of the stress close to rough surfaces, and that the relative magnitude of the sweep component increases both with surface roughness and with proximity to the surface. The sweep-dominated region delineates a ‘roughness sublayer’ with a depth of up to several roughness element heights, in which the turbulence characteristics depend explicitly on the roughness. In the remainder of the inner (or constant-stress) layer, and in the outer layer, the flow obeys familiar similarity laws with respect to surface roughness.

The difference ΔS0 between the fractional contributions of sweeps and ejections to the stress is shown to be well related everywhere to the third moments of the streamwise and normal velocity fluctuations. Experimental proportionalities are established between the third moments and δS0, and are shown to agree with predictions made from cumulant-discard theory.

The time scale for the passage of large coherent structures past a fixed point, T, is assumed proportional to the mean time between occurrences in a specified quadrant of an instantaneous stress u'w’ at least H times the local mean stress u'w’, where H is a threshold level. For both the ejection and sweep quadrants and for any choice of H, it is found that T scales with the friction velocity u* and the boundary-layer thickness δ, such that Tu*/δ is invariant with change of surface roughness.

Shock reflections over a convex and a concave wedge were investigated by using a 5 × 7 cm ordinary pressure-driven shock tube. Dry air was used for both the driving and driven gases. The large difference between the transition from regular (RR) to Mach reflection (MR) and that from MR to RR was observed, confirming the results obtained by Ben-Dor, Takayama & Kawauchi (1980). These results contradict all of the previous theoretical transition criteria. A new theory on the transition between RR and MR was developed by applying Whitham's ‘ray shock’ theory. This new theory agrees quite well with the experimental results.

The so-called ‘water-bag’ method is used to study the behaviour of a two-dimensional inviscid layer of constant vorticity ω and of mean thickness δ adjacent to a wall with slip at the wall. A nonlinear initial-value equation is derived which describes the motion of the material interface separating the rotational fluid within the layer from the irrotational free stream, for the case where this interface is subject to streamwise cyclic disturbances to its undisturbed shape. A linearized solution to this equation shows that a sinusoidal disturbance of wavelength λ propagates as one mode of a neutrally stable Kelvin-Helmholtz wave with velocity ωλ[1 − exp (−4πδ/λ)]/4π relative to the fluid at infinity. Numerical solutions of the full nonlinear equation for a range of wavelengths and finite disturbance amplitudes indicate different behaviour. For sufficiently large amplitude the interface valleys evolve into long re-entrant wedges of irrotational fluid which are ‘entrained’ into the layer and which are separated from the free stream by lobes or bulges of rotational fluid. This single-mode nonlinear interfacial distortion could be generated over a broad wavelength range with no indication of preferential scaling based on δ. It is suggested that the interface behaviour bears distinct resemblance to flow features observed at the interface between turbulent and non-turbulent fluid in recent smoke-in-air flow-visualization studies of the outer part of a constant pressure turbulent boundary layer. The calculated rotational fluid lobe velocities, which are not very different from the equivalent linearized wave velocities, are found to be in reasonable agreement with the few existing measurements of the velocity of bulges at the turbulent–nonturbulent fluid interface, while the computed velocity field in the lobe is in qualitative agreement with the general flow pattern observed in experiments. In the absence of a preferred scale or range of scales for the development of the interfacial distortion, however, it is concluded that the present results cannot be interpreted as supporting the hypothesis of the presence of largescale coherent motions in the outer part of the layer.

An approximate, conveniently applied theory with corresponding experimental data is presented concerning the changes in momentum and mass transfer produced by a ridge of small slopes in a flat-surface quasi-stationary turbulent boundary layer. A first-order mean velocity perturbation solution is found to be in good agreement with measured velocities on the up-slope side of a two-dimensional ridge, of length 20 cm and height 1 cm, fixed on the floor of the working section of an open-circuit wind tunnel. A vapour-transfer eddy-diffusivity distribution is then calculated for the inner boundary-layer region and solutions of the consequent vapour-transfer equation give the variation of rate of evaporation from surfaces of varying lengths placed at different positions on the up-slope region of the ridge. Corresponding measurements are found to be in good agreement with the theoretical calculations, and show that, even over small slopes (of 1 in 10), the evaporation rate varied with position by 25% from maximum to minimum. This method of calculation is extended to examine the effect of surface curvature on diffusion of gas from an upstream line source in a turbulent boundary layer over the ridge; experimental and theoretical concentration profiles compare extremely well over the leading slope.

The diffraction of externally generated sound in a uniformly moving flow at the trailing edge of a semi-infinite flat plate is studied. In particular, the coupling of the sound field to the hydrodynamic field by way of vortex shedding from the edge is considered in detail, both in inviscid and in viscous flow.

In the inviscid model the (two-dimensional) diffracted fields of a cylindrical pulse wave, a plane harmonic wave and a plane pulse wave are calculated. The viscous proess of vortex shedding is represented by an appropriate trailing-edge condition. Two specific cases are compared, in one of which the full Kutta condition is applied, and in the other no vortex shedding is permitted. The results show good agreement with Heavens’ (1978) observations from his schlieren photographs, and confirm his conclusions. It is further demonstrated, by an explicit expression, that the sound power absorbed by the wake may be positive or negative, depending on Mach number and source position. So the process of vortex shedding does not necessarily imply an attenuation of the sound.

In the viscous model a high-Reynolds-number approximation is constructed, based on a triple-deck boundary-layer structure, matching the harmonic plane wave outer solution to a known incompressible inner solution near the edge, to obtain the viscous correction to the Kutta condition.

The stability characteristics for spatially periodic parallel flows of an incompressible fluid (both inviscid and viscous) are studied. A general formula for the determination of the stability characteristics of periodic flows to long waves is obtained, and applied to approximate numerically the stability curves for the sinusoidal velocity profile. The neutral curve for the sinusoidal velocity profile is obtained analytically. The stability of two broken-line velocity profiles in an inviscid fluid is studied and the results are used to describe the overall pattern for the sinusoidal velocity profile in the case of long waves. In an inviscid fluid it is found that all periodic flows (other than the trivial flow in which the basic velocity is constant) are unstable to long waves with a value of the phase speed determined by simple integrals of the basic flow. In a viscous fluid it is found that the sinusoidal velocity profile is very unstable with the inviscid solution being a good approximation to the solution of the viscous problem when the value of the Reynolds number is greater than about 20.

Some theorems concerning the vorticity in barotropic flows of perfect fluids are generalized for non-barotropic flows. The generalization involves replacing the velocity in certain parts of the equations by a time-dependent quantity which is a function of the velocity and thermodynamic properties of the fluid. Results which are generalized include Kelvin's circulation theorem and conservation laws for potential vorticity and helicity. It is shown how the results can be further generalized to include dissipative effects. The possibility of using some of the results in deriving a complete set of Lagrangian conservation laws for perfect fluids is discussed.

The analysis of Acrivos & Herbolzheimer (1979) is extended to describe the sedimentation of dilute suspensions in tilted two-dimensional channels in which the spacing between the plates is small compared with their length. The theory assumes that the flow is laminar and that the suspension consists of monodisperse spherical beads having small particle Reynolds number. Expressions for the flow fields in the clearfluid region and in the suspension, as well as for the location of the interface separating these two regions, are obtained asymptotically in the limit of Λ [Gt ] 1 with $R\Lambda^{-\frac{1}{3}}\ll 1$, where R and A are as defined in the previous work. The present analysis differs from that given earlier in that the aspect ratio, i.e. the ratio of the height of the suspension to the channel width, is now taken to be O(A1/3) rather than O(1) as was the case before. Under these conditions, the solution of the time-dependent equations leads to the surprising prediction that the clear-fluid layer which forms beneath the downward-facing plate attains a steady shape only along the lower portion of the channel while, in contrast, its thickness increases with time for locations along the channel that are above some critical point. Because of this transient behaviour, the well-known Ponder-Nakamura-Kuroda (PNK) formula overestimates the rate at which the top of the suspension region falls with time; however, the PNK results for the volumetric settling rate still hold under the conditions considered in this paper. It is shown that this discontinuity in the interface shape can be suppressed in continuous settling systems but only if the feed and withdrawal locations are chosen properly.

Batch sedimentation experiments were conducted in a channel with parallel flat walls under the following sets of conditions: H0/b ≈ 90, 5° ≤ θ ≤ 45°, 0·01 ≤ c0 ≤ 0·025, 1·7 × 107 < Λ < 3·5 × 107, and 1·8 < R < 2·1, where θ is the angle of inclination of the vessel from the vertical, and c0 is the initial volume fraction of solids in the suspension. The experimental observations were found to be in excellent agreement with the theoretical predictions.