Using the assumptions of an incompressible and viscous flow at large Reynolds number, we derive the evolution equation for the wave action density of an instability wave travelling on top of a laminar free-shear flow. The instability is considered to be viscous; the purpose of the present work is to include the cumulative effect of the (locally) small viscous correction to the wave, over length and time scales on which the underlying base flow appears inhomogeneous owing to its viscous diffusion. As such, we generalize our previous work for inviscid waves. This generalization appears as an additional (but usually non-negligible) term in the equation for the wave action. The basic structure of the equation remains unaltered.

The disturbances on the free surface of dielectric fluids resulting from intense laser heating of their boundary layer are studied theoretically and experimentally. The heating is accompanied by pronounced evaporation from the surface and thereby leads to a recoil pressure momentum applied to the surface. For small values of total momentum transferred to the fluid, the low-amplitude initially hollow-like displacement of the surface in the impact zone decays to produce linear gravity–capillary waves (GCW) spreading out on the surface. This regime is treated analytically and the results obtained are compared with experiments involving weakly viscous (water, ethanol) and highly viscous (glycerol) liquids. An experimental arrangement for remote generation and subsequent detection of probe GCW-packets is given. The evolution of broadband GCW-disturbances on clean and surfactant-contaminated water surfaces are described. Results of GCW-attenuation spectrum measurements on clean water surfaces and on film-covered surfaces are presented.

High total recoil momentum values give rise to substantially nonlinear surface motion: after a short transient stage the surface takes the shape of a hemisphere expanding into the liquid, and later the liquid above the hemisphere closes up to form a cavity and slow down the expansion. For this regime the dynamics of the hemisphere expansion are determined and satisfactory agreement with experimental data obtained with the shadowgraph technique is established. Consistency of theory and experiment allowed the determination of the total recoil pressure momentum and its surface distribution.

In the intermediate case of moderate values of recoil momentum, the nonlinear evolution of broadband GCW-packets on clean and surfactant-contaminated water surfaces is investigated experimentally.

Higher-order nonlinear corrections to the Stokes pendulum problem are calculated in perturbation schemes for small values of Reynolds numbers R(2) = umd0/2ν. Here the controlling lengthscale ½d0 is the displacement amplitude of the undisturbed periodic motion, um is the velocity amplitude and ν is the kinematic viscosity. Solutions for two general types of periodic motion are found; namely orbital motion as under deep water waves and oscillatory motion as under shallow water or acoustic waves. These solutions are found by matched asymptotic expansions using the fundamental irrotational oscillation to drive a thin Stokes a.c. boundary layer over the surface of the sphere. From the boundary layer several secondary motions are excited which die away in the neighbouring fluid. Among these are an orthogonal system of steady, rotational Eulerian streaming currents, and two outwardly radiating non-dispersive waves, one having the frequency of the fundamental but with a phase shift, the other appearing at the second harmonic.

With these solutions the forces and torques on a fixed sphere were computed. One of the orthogonal components of the rotational streaming field was found to produce a rotary lift force which opposed virtual-mass forces and diminished the resultant force component in quadrature to the fundamental oscillation. The other streaming component contributed damping terms which, unlike leading-order Stokes drag, vary nonlinearly with the displacement amplitude. Steady and second-harmonic torques were found to act on the sphere about the horizontal axis transverse to the fundamental oscillation.

It is shown that the vortex filament in background shear considered in Aref & Flinchem (1984) is unstable to infinitesimal disturbances, and that the numerical results described therein are consistent with the characteristics of the instability.

A liquid-metal flow impinging upon a region of non-uniform d.c. magnetic field experiences a certain amount of braking owing to the effect of Lorentz forces acting on the metal. Practical electromagnetic flow control devices utilize this property to alter the flow rate at which a liquid metal emerges from a receptacle. As a preliminary step to understanding the three-dimensional behaviour a numerical model is constructed which examines the two-dimensional flow of liquid metal passing through a quadrupole magnetic field generated by four line currents. In the vicinity of the local neutral point it is found that the nonlinear flow becomes unidirectional and linear. This linear behaviour agrees well with analytic solutions for flow through an infinitely extended neutral point. The generalized forms of the magnetic fields which permit unidirectional flows to exist are investigated in both axisymmetric and two-dimensional geometries. Examples of these fields include both the extended neutral point and the uniform transverse magnetic field present in Hartmann flow. The optimum conditions for braking the flow with a specified field are characterized by the pressure and volume data. These variables are derived from the model for a range of values of field strengths and Reynolds numbers and allow a comparison to be made with the asymptotic results obtained from the linear theory for two-dimensional flows. The numerical scheme may be adapted for any type of magnetic field and also permits extensions to the more realistic axisymmetric case.

A theory is developed for analysing the inviscid interpenetration of two streams. It is assumed that the difference in total pressure between the streams is not large. Several examples of the general results are presented.

An approach utilizing multiple scales and matched asymptotic expansions is developed for the description of small perturbations at large distances from a thin airfoil oscillating harmonically in a uniform supersonic flow. The problem of determining the unsteady perturbation potential is formulated in general, and an analytical solution is derived for an airfoil with parabolic or flat surfaces. The results describe the flow ahead of the region influenced by the trailing edge. The variation in the pressure jump across an attached leading-edge shock wave is also obtained.

A uniformly valid theory (all wavelengths and angles of incidence) for the diffraction of sea waves by a slender body, correct to second order in the slenderness parameter, has been derived for the shallow-water limit. This theory is now extended to the finite water depth case, with the same results and accuracy.

Laminar flow through slots is investigated using a flow-visualization technique and the numerical solution of the Navier-Stokes equations for steady flow. In the flow situation studied here, the fluid enters an upper channel blocked at the rear end and leaves through a lower channel blocked at the front end. The two channels are interconnected by one, two and three slots. The flow-visualization technique effectively brings out the various features of the flow through slot(s). The ratio of the slot width to the channel height w/h is varied between 0.5 to 4.0 and the Reynolds number Re, based on the velocity at the entry to the channel and the height of the channel, is varied between 300 and 2000. Both w/h and Re influence the flow in general and the extent of the regions of recirculating flow in particular. The Reynolds number at which the vortex shedding begins depends on w/h. Computations are carried out using the computer code 2/E/FIX of Pun & Spalding (1977). The computed flow patterns closely resemble the observed patterns at various Reynolds numbers investigated except around the Reynolds number where the vortex shedding begins.

An experimental study of the flow past a thin finite length plate in a supersonic low density stream is reported. The paper discusses the corrections that are necessary for surface pressures measured under rarefied conditions. It is shown that the recent method of ‘orifice’ corrections due to Harbour & Bienkowski is versatile and reliable to use for both cold wall and insulated wall measurements. For the conditions of the experiment, the flow over the plate was found to be dominated by both leading-edge and trailing-edge interactions.

The structure of a shock wave in a vibrationally relaxing gas undergoing reflexion from a plane wall is examined. The shock wave is assumed to be weak, and departures from thermodynamic equilibrium are assumed small; both an adiabatic and an isothermal wall are considered. The flow field is divided into three regions: a far-field region, an interaction region, and, for the isothermal-wall case, a thermal boundary layer. Different asymptotic expansions are determined for the various regions through the method of matched asymptotic expansions. In the region far from the wall, a non-equilibrium Burgers equation governs the motion and the incident and the reflected shock wave structures. During reflexion, a non-equilibrium wave equation applies; its first-order terms are equivalent to an acoustic approximation. Heat conduction to the wall is modelled by an isothermal wall boundary condition which requires the introduction of a thermal boundary layer adjacent to the wall. This thermal boundary layer is thin and the adiabatic-wall result provides the outer solution for treating this layer. This thermal layer affects the structure of the reflected wave.