A numerical calculation is presented for the slow flow of a viscous fluid in a region bounded by a right-angled isosceles triangle. The particular flow considered is the secondary flow generated in the plane of a cross-section by the primary axial flow, under a constant pressure gradient, through a slightly curved tube of triangular cross-section. The flow is assumed to be at small Dean number so that the stream function of the secondary flow satisfies the biharmonic equation. The sequence of eddies of decreasing size and intensity first identified by Moffatt (1964a) is observed in each of the corners. Numerical details of a number of these eddies are given and their properties are found to be in excellent agreement with the theory.

The method developed previously (Youngren & Acrivos 1975) for obtaining numerical solutions to the Stokes equations for flows past solid particles is extended to problems with free boundaries. This technique is applied to the determination of steady shapes for an inviscid gas bubble symmetrically placed in an extensional flow. For large surface tension the computed bubble shape is found to be in excellent agreement with that obtained analytically by Barthès-Biesel & Acrivos (1973), while for small surface tension it agrees with an expression derived by Buckmaster (1972) using slender-body theory.

In typical jet-noise measurements one is almost always interested in the pressure in the far field as kR → ∞. The purpose of this paper is to show that this limit is singular in the sense of matched asymptotic expansions. The inner solution (kfixed, R→ ∞) is given by geometric acoustics, whereas the outer is given by the so-called acoustic-shielding solution (k fixed, R→ ∞). A suitable composite solution is also constructed.

Now jet-noise measurements are always made at fixed and finite values of R (typically 50 jet diameters) and from these measurements one would like to infer the value of pR at R = ∞, where p is the acoustic pressure. One interesting and somewhat unexpected result of this paper is that the value of pR at infinity cannot be inferred from these measurements above a certain frequency. In other words, in order to obtain accurate estimates of pR at infinity for higher and higher frequencies, one has to be further and further away from the jet!

A stability analysis of meandering and braiding perturbations in a model alluvial river is described. A perturbation technique, involving a small parameter representing the ratio of sediment transport to water transport, is used to obtain the following results.

Under appropriate conditions, the existence of sediment transport and friction are necessary conditions for the occurrence of instability in the flow and on the bed; thus instability is not inherent in the flow alone. An Anderson-type scale relation for longitudinal instability is obtained for meandering. A relation estimating the number of braids and differentiating between meandering and braided regimes is derived. These relations are independent of sediment transport.

This paper is concerned with convection generated by uniformly distributed internal heat sources. By a numerical method it is found that the planform is down-hexagons for infinite Prandtl numbers and Rayleigh numbers up to at least 15 times the critical value. The motion is also studied for finite Prandtl numbers and small supercritical Rayleigh numbers by using an amplitude expansion. It turns out that a small subcritical regime exists. Moreover, it also emerges that for Prandtl numbers less than 0.25 the stable planform is up-hexagons. In §3 a necessary condition in order to obtain a hexagonal planform is derived when the coefficients in the differential equations are a function of the vertical co-ordinate z.

The stress relaxation effect in an incompressible elastico-viscous fluid is investigated for the case of the lubrication of line-contact rollers. Two extreme cases are considered: that of low pressures with rigid surfaces and constant viscosity and that of heavily loaded elasto-hydrodynamic lubrication. In order to solve this problem, a new invariant material time derivative is suggested. This derivative is referred to a co-ordinate system attached to the principal axes of the strain-rate tensor, while the former derivatives have been referred to the fluid particle. It is shown that, unlike the previous derivatives, the new one enables a separate parametric description of the stress relaxation process and the first normal-stress difference. The results show that a significant increase in the load capacity is obtained, owing to the relaxation time of the fluid. The investigation is for fluids with a relaxation time small compared with the transit time of the lubricant through the bearing.

This paper reports an experimental investigation of pressure and force distributions on a sharp-nosed circular cylinder inclined to a uniform low-speed air flow under conditions of laminar separation of the boundary layer. The main concern is with the out-of-plane force (i.e. the side force if the body is at incidence). The experimental model consisted of an extensively pressure-tapped cylinder to which four different noses were fitted. The results show that there is an oscillatory distribution of out-of-plane force along the cylinder for most of the inclination range 0-90°. The amplitude of this distribution is strongly affected by nose shape in conditions where the out-of-plane force extends onto the nose. At very high angles of inclination the oscillatory distribution disappears and is replaced by a vortex pattern like that found on an infinite yawed cylinder. The general nature of the out-of-plane force is found to be consistent with the impulsively started flow analogy. Unsteadiness in the flow was found to cause a serious reduction in many of the time-averaged values. The unsteadiness is ascribed to the switching of the flow pattern due to free-stream turbulence. Measurements of the time histories of certain pressures enabled values of the force in the unswitched state to be calculated. The Reynolds number was found to have an important influence at inclinations above 55°. However, it was also found that the range of Reynolds numbers over which this effect occurs can depend on the scale of the model.

Large coherent eddies have been observed in turbulent shear layers and seem to play an important role in their growth, mixing and noise production. Winant & Browand (1974) have observed that the pairing of large eddies is central to the question of shear-layer development, and they model the pairing process with discrete line vortices. It is shown here that the growth of the layer and amalgamation of large eddies are not adequately treated by isolated-line-vortex models, which are proved to be essentially non-evolutionary. A more detailed model of the shear layer, itself consisting of vortex elements, is shown to provide the definition required to observe the evolution and coalescence of the large eddies. The observed development of this model shear layer is consistent with many features of experimentally observed flows.

Supersonic nozzle flows of a condensable vapour are considered in the high activation limit for homogeneous nucleation. Conditions are determined under which the final collapse of the supersaturated state is described by a condensation shock. It is shown that the shock zone is associated with droplet growth: droplet production occurs in a thin layer upstream of the growth region. Some new scaling laws are obtained for the structure of the production layer.