Grid turbulence convected by a free stream past a rigid surface moving at the same speed as the free stream is analysed by boundary-layer theory and spectral methods. The turbulence is assumed to be weak, i.e. $u^{\prime}_{\infty}/\overline{u}_{\infty}\ll 1$ and its Reynolds number to be large, i.e. $u^{\prime}_{\infty}/\overline{u}_{\infty}\gg 1$ where u′∞ is the r.m.s. turbulent velocity. Two regions are found to exist. The outer, source region B(s) has a thickness of the order of the integral scale L∞. Here the normal component of turbulence decreases and the lateral and streamwise components are amplified. The inner, viscous region B(v) has thickness $[x\nu/\overline{u}_{\infty}]^{\frac{1}{2}} $, where x, v and $\overline{u}_{\infty} $ are the streamwise co-ordinate, kinematic viscosity and mean velocity respectively. Here the turbulent velocity decays to zero at the surface. Spectra variances and cross-correlations are calculated and found to compare well with measurements of turbulence near moving walls by Uzkan & Reynolds (1967) and Thomas & Hancock (1977).

The results of this theory are shown to have a number of applications including the prediction of turbulence near wind-tunnel walls and near flat plates placed parallel to the flow.

A set of constitutive equations is derived to describe the time-dependent flow of a dilute suspension of identical rigid particles of arbitrary shape which are influenced by Brownian couples. The form of the orientation probability distribution for small departures from isotropy is found. The case of weak flows with strong Brownian effects is studied in detail, and the viscoelastic approximation and second-order-fluid limit of the constitutive equation are derived for a general particle shape. A full numerical solution is given for ellipsoids. The general nearly spherical particle is also considered and constitutive equations for general flow strengths are obtained for this case.

Brenner's general results for the force and torque experienced by an arbitrary particle simultaneously translating and rotating in a linear shear flow are applied to the spherical cap. The cap's five fundamental resistance tensors are determined and the corresponding tensors for the sphere and circular disk are recovered as special cases. The problem of a freely moving cap in a linear shear is considered and the resulting translational and rotational motions are analysed. The cap's centre of free rotation is found and trajectories of this point are plotted in a few instances. The cap is also found to possess a ‘point of planar motion’ which always moves in a plane perpendicular to the vorticity vector of the undisturbed shear regardless of the initial orientation of the cap. It is shown that the motion of the cap actually serves as a model for the motions of all ‘oblate’ asymmetric bodies of revolution which are moving freely in a linear shear.

One of the main problems in welding is to produce consistent weld profiles. Simple heat-flow models of the weldpool, which are currently used to predict the shape of the solid-liquid boundary, do not take account of fluid motion which is observed in practice and the effect of such motion could be significant. Electromagnetic j × B forces due to the welding arc have been proposed as a major cause of the motion and we attempt here to develop existing flow models towards more practical welding situations. We consider the steady-state flow of an incompressible viscous conducting fluid in a hemispherical container due to various axisymmetric representations of the distributed current sources which can arise in arc welding. A solution is found for sufficiently small currents that inertial effects may be ignored and no singularities appear in the velocity field. We discover that varying the current distribution can lead to qualitatively different flow patterns, i.e. poloidal flows in opposite directions and breakup into two distinct counter-rotating loops.

Bulk-coupled instability at the interface between miscible fluids which have identical mechanical properties but disparate electrical conductivities and are stressed by an equilibrium normal electric field is studied experimentally and theoretically. Observations of fluid motions permit measurement of an instability wavenumber and growth rate.

A model with a layer of diffusive conductivity distribution coupled to uniform bounding half-spaces is developed. Numerical integration of linearized electromechanical equations leads to a set of growing eigenfrequencies with corresponding eigenmodes, pure real for small wavenumber and complex (propagating) for large wavenumber.

The fastest growing wavenumber and corresponding growth rate are characterized as a function of the conductivity ratio and a time-constant ratio, which reflects the importance of inertial and viscous effects. In the viscous-dominated limit, the description agrees with a corresponding surface-coupled theory. The model is evaluated for parameters corresponding to experimental observations.

In this paper we obtain an explicit representation for the unsteady motion on a transversely sheared mean flow that corresponds to the gustline motion on a uniform mean flow. The important features of this motion are discussed. It is shown that its velocity, pressure and vorticity are all induced by a certain disturbance field that is a linear combination of the vorticity and particle-displacement fields and is everywhere frozen in the mean flow. The general ideas are illustrated by considering the scattering of a gust by a half-plane embedded in a shear flow.

Spark photography with a sensitive schlieren system has been used to show the interaction between an incident acoustic wave and the flow around an airfoil trailing edge. Impact of the wave did not show any significant observable effect on the wake or trailing-edge boundary layer. The intensity of the wave diffracted from the edge varied considerably with the prevailing flow conditions. In the event of unsteadiness in the flow or boundary-layer separation the diffracted wave was strongly visible. In smooth flows with attached boundary layers the diffracted wave was very weak. These observations tend to support the recent conclusion of Howe (1976) that trailing-edge flows are quieter if they do not show singular behaviour. This is in contrast to the predictions of earlier theoretical models of the edge diffraction problem.

Water-wave experiments are presented showing the evolution of finite amplitude waves in relatively shallow water when no solitons are present. In each case, the initial wave is rectangular in shape and wholly below the still water level; the amplitude of the wave is varied. The asymptotic solution of the Korteweg-de Vries (KdV) equation in the absence of solitons (Ablowitz & Segur 1976) is compared with observed evolution. In addition, the asymptotic solution of the linearized KdV equation (a linear dispersive model) is compared with both the KdV solution and experiments. This comparison is a natural consequence of the fact that, in the absence of solitons, the asymptotic solutions of the KdV equation and its linearized version are qualitatively similar. Both the experiments and the model equations suggest that the asymptotic wave structure consists of a negative triangular wave, travelling with a speed (gh)½, followed by a train of modulated oscillatory waves which travel more slowly. Quantitative comparisons are made for the amplitude, shape and decay rate of the leading wave and the amplitude, dominant wavenumbers and velocities of the trailing wave groups. Over the parameter range of the experiments, asymptotic KdV theory predicts more closely the observed behaviour. The leading wave is observed to decay more rapidly than the trailing wave groups; hence the leading wave becomes less prominent with time. This is in agreement with the KdV solution, whereas just the opposite is predicted by linear theory. Linear predictions for the trailing wave groups are accurate only when they agree with the KdV predictions. Both models predict the evolution of short waves in the trailing wave region. When the short waves are unstable (k gt; 1·36), either group disintegration or focusing into envelope solitons is possible. Both of these phenomena are observed in the experiments; neither is predicted by long-wave models. The nonlinear Schrödinger equation is reviewed and tested as a model of these unstable wave groups. There is some evidence that the KdV equation and the nonlinear Schrödinger equation can be patched together to provide an asymptotic description of these unstable groups.

Model equations which describe the evolution of long-wave initial data in water of uniform depth are tested to determine explicit criteria for their applicability. We consider linear and nonlinear, dispersive and non-dispersive equations. Separate criteria emerge for the leading wave and trailing oscillations of the evolving wave train. The evolution of the leading wave depends on two parameters: the volume (non-dimensional) of the initial data and an Ursell number based on the amplitude and length of the initial data. The magnitudes of these two parameters determine the appropriate model equation and its time of validity. For the trailing oscillatory waves, a local Ursell number based on the amplitude of the initial data and the local wavelength determines the appropriate model equation. Finally, these modelling criteria are applied to the problem of tsunami propagation. Asymptotic (t → ∞) linear dispersive theory does not appear to be applicable for describing the leading wave of tsunamis. If the length of the initial wave is approximately 100 miles, the leading wave is described by a linear non-dispersive model from the source region until shoaling occurs near the coastline. For smaller lengths (∼ 40 miles) a linear dispersive (but not asymptotic) model is applicable. The longer-period oscillatory waves following the leading wave, which can induce harbour resonance, apparently require a nonlinear dispersive model.

The problem of a liquid jet moving at hypersonic speed into a gas is considered in a frame of reference in which the tip of the jet is at rest. The liquid jet flow is assumed to be inviscid, irrotational, incompressible and two-dimensional although an approximate extension to the axially symmetric case is developed. The air flow in the hypersonic shock layer is analysed using the modified Newtonian theory. The condition of continuity of pressure at the gas-liquid interface then allows a solution to the potential problem in the liquid to be found by transforming to the hodograph plane. The resulting jet shape is presented graphically in terms of the relevant parameters.

The application of the method to penetration problems is also discussed and comparisons made with experimental results and ‘exact’ solutions.

We consider a compressible laminar boundary layer with uniform pressure when x < x0 and a prescribed large adverse pressure gradient when x > x0. The Illingworth-Stewartson transformation is applied, and the transformed external velocity u1(x) then chosen such that \[ \lambda = -\frac{x_0}{u^2_0}u_1\frac{du_1}{dx}\frac{T_w}{T_s} \] is constant, where Ts is the stagnation temperature.

For large λ, when a thin sublayer exists as the layer reacts to the sharp pressure gradient, inner and outer asymptotic expansions are derived and matched for functions F and S which determine the stream function and the temperature. The equations for F and S are largely uncoupled, in that the first approximation to F is independent of S, the first approximation to S depends only on the first approximation to F, and so on.