In arc welding electromagnetic forces are thought to be the major cause of motion in the weldpool, and it has recently been found by experimentalists that the application to the workpiece of a uniform magnetic field normal to the weldpool surface appears to stabilize the welding process. In this paper we investigate motion in a hemisphere due to a stationary distributed current source with a superimposed uniform magnetic field applied parallel to the axis of symmetry. When inertial effects are ignored and a simple source-sink model of the current source is introduced, we obtain an analytic solution for the fluid flow valid for low currents and low applied fields. A numerical scheme is then developed to solve the full nonlinear-flow problem and results are obtained for the source-sink model of the current source and for a more realistic numerically constructed distributed current source. For values of the externally applied magnetic field and the current flowing through the hemisphere typical of those occurring in practical welding situations we discover that the flow in an axial section through the pool is radially outwards on the free surface. This is in the opposite direction to that generally predicted by the theory when there is no superimposed magnetic field.

Decaying turbulence in neutral and stratified fluids has been studied experimentally for relatively high mesh Reynolds numbers and long time-histories. The neutral case indicates an initial period decay law, q2∝ t−1, through non-dimensional time \[ W_gt/M \simeq 800 \] which is considerably longer than previous measurements at the same mesh Reynolds number (Re = 48260). The stratified experiment resulted in a decay rate virtually identical to that of the neutral case through Wgt/M = 275. However the decay rate sharply decreased after this time when the field of turbulence was replaced by internal gravity waves. A critical Richardson number marks the transition from the turbulence to an internal gravity wave domain.

The diffraction of a steady Stokes wave train by a thin wedge with vertical walls is studied when the incident wave is directed along the wedge axis (grazing incidence). Parabolic approximation applied recently by Mei & Tuck (1980) to linear diffraction is extended to this nonlinear case. Significant effects of nonlinearity are found numerically, in particular the sharp forward bending of wave crests near the wedge. The computed features are found to corroborate the existing experiments only qualitatively; the controlling factors in the latter being not completely understood. An analytical model of stationary shock is proposed to approximate the numerical results of Mach stems.

A diagnostic visualization study of turbulence in stagnation flow around a circular cylinder was carried out to gain physical insight into the coherent structure of turbulence in flow around a bluff body advanced by the vorticity-amplification theory. The visualization was conducted at a cylinder-diameter Reynolds number of 8 × 103 utilizing titanium dioxide white smoke for an approaching flow containing turbulence at scales larger than the neutral wavelength of the stagnation flow. Analyses of the flow events focused on tracing out the temporal and spatial evolution of a cross-vortex tube outlined by the entrained smoke filaments from its emergence near the stagnation zone through its penetration into the cylinder boundary layer.

The selective stretching of cross-vortex tubes, their streamwise tilting, the emergence of an organized turbulent flow pattern near the stagnation zone, the interaction of the amplified vorticity with the body laminar boundary layer and the growth of a turbulent boundary layer were revealed by the visualization. In particular, the visualization indicated that the cross-vortex tubes conveyed by the diverging stagnation flow constitute a coherent substructure within the overall turbulent flow that is triggered to its fullest manifestation by the stretching mechanism.

This paper considers the nature of stationary axisymmetric convection in a shallow rotating annulus or cylinder heated from below. The horizontal and vertical walls of the container are assumed to be perfect conductors and insulators respectively. The critical regime is considered in which the circulations due to the centrifugal force and the vertical gravitational instability are of equal significance. Among the effects of the centrifugal acceleration on the gravitational instability are a shift in the value of the Rayleigh number at which instability sets in, a modification in the distribution and amplitude of convection cells in the container and, most significantly, a smooth transition to finite amplitude convection as the Rayleigh number is increased.

The buoyancy flux ratio, r = αFT/βFS, across a salt-sugar fingering interface is determined from accurate measurements of the density variations in a two-layer run-down experiment. Since r is close to 1, the net buoyancy flux, βFS − αFT, which is proportional to 1 − r, gives r with a resolution that is much improved over that of previous measurements. The value of r is found to decrease from r ≈ 0·94 ± 0·01 at Rρ = 1·02 to r = 0·88 ± 0·01 at Rρ = 2, where Rρ is the density anomaly ratio. The latter is smaller than the previous (constant) value of 0·92. The buoyancy flux due to sugar is found to decrease rapidly with increasing Rρ, varying approximately as R−6ρ.

The energetics of a linear array of hollow or stagnant-cored vortices of finite cross-section in an ideal fluid is studied in this paper. The results are useful in a discussion of the amalgamation of vortex structures in a turbulent mixing layer.

Solutions to the steady advection–diffusion equation in a branching channel are obtained for both uniform and spatially varying flow fields and for two channel geometries. An interesting feature of the solutions is that anisotropy of the dispersion coefficients in the direction of the streamlines may be accounted for. The analysis reveals that mixing is confined to a distance, b2U/π2KN, downstream of the junction in the advection-dominated case and a distance, KS/U, upstream in the diffusion-dominated situation, KS and KN being the diffusivities along and across the flow respectively, U the characteristic velocity of the flow, and b the breadth of channel downstream of the junction.

Flow visualization and laser-doppler anemometry have been used to determine the flow structure and measure the velocity distribution inside a rotating cylindrical cavity with an outer to inner radius ratio of 10, and an axial spacing to inner radius ratio of 2·67. A flow structure comprising an inner layer, Ekman layers, an outer layer and an interior potential core has been confirmed for the cases where the inlet air enters the cavity either axially, through a central hole, or radially, through a central gauze tube, and leaves radially through a series of holes in the peripheral shroud. Velocity measurements in the laminar Ekman layers agree well with the ‘modified linear theory’, and long-and short-wavelength disturbances (which have been reported by other experimenters) have been observed on the Ekman layers when the radial Reynolds number exceeds a critical value. The phenomenon of reverse flow in the Ekman layers and the possibility of ingress of external fluid through the holes in the shroud have also been observed.

An efficient relaxation method is developed for computing the properties of a family of vortex pairs with distributed vorticity, propagating without change of shape through a homogeneous, inviscid fluid. The numerical results indicate that a steady state exists even when the gap between vortices is arbitrarily small, and that as the gap closes the steady state approaches a limiting vortex pair with a cusp on the axis of symmetry. Comparison is made with an approximate theory due to Saffman, and agreement is found to be good until the vortices are almost touching. The energy of members of the family is computed, and possible means of experimental production are discussed.

By the use of Green's theorem, relations are derived for the interaction of regular waves with a body in a canal. These relations are then applied to the problem of wave-power absorption by a body in a canal; this being taken as a model of an infinite row of wave-power absorbers. Two particular shapes of wave-power absorber are studied by use of thin-ship approximation. It is shown that the efficiency of power absorption by. a body in a canal may be much reduced when there is more than one travelling wave mode present in the canal.

A useful parametrical model for the vertical structure of the pressure field induced by wind blowing over a field of surface gravity waves is proposed. The model is a linear expansion in a set of empirical orthogonal functions, derived from a set of 110 complex pressure profiles computed according to the theory of Miles (1957), and provides a compact, quantitative description of those profiles. The model has been used as an element in the analysis of a body of experimental data on wave-induced atmospheric pressure fluctuations obtained by Snyder et al. (1980).

A nonlinear three-dimensional boundary-layer problem governing the flow upstream of a particular disturbance (e.g. a shallow obstacle) at the wall is considered. The upstream response, a free interaction, takes place under zero displacement of the boundary layer, and the solution is found numerically using Fourier series truncation and varying the number of terms kept in the series. In one part of the flow field regular separation is encountered, beyond which the motion becomes strongly attached to the wall elsewhere in the flow field. Analytically, local structural investigations then suggest that the attached part of the upstream response terminates at a line singularity, while the separated part can continue indefinitely far downstream. The former structure leads to a new set of similarity solutions of the three-dimensional boundary-layer equations, while the latter develops a vortex sheet formation. The three-dimensional flow problem has most relevance to pipe flows, but some connexion also with external flows, and the implications for these are discussed.