The flow in a channel with an oscillating constriction has been studied by the numerical solution of the Navier-Stokes and Euler equations. A vorticity wave is found downstream of the constriction in both viscous and inviscid flow, whether the downstream flow rate is held constant and the upstream flow is pulsatile, or vice versa. Closed eddies are predicted to form between the crests/troughs of the wave and the walls, in the Euler solutions as well as the Navier-Stokes flows, although their structures are different in the two cases.

The positions of wave crests and troughs, as determined numerically, are compared with the predictions of a small-amplitude inviscid theory (Pedley & Stephanoff 1985). The theory agrees reasonably with the Euler equation predictions at small amplitude (ε [lsim ] 0.2) as long as the downstream flow rate is held fixed; otherwise a sinusoidal displacement is superimposed on the computed crest positions. At larger amplitude (ε = 0.38) the wave crests move downstream more rapidly than predicted by the theory, because of the rapid growth of the first eddy (‘eddy A’) attached to the downstream end of the constriction. At such larger amplitudes the Navier-Stokes predictions also agree well with the Euler predictions, when the downstream flow rate is held fixed, because the wave generation process is essentially inviscid and the undisturbed vorticity distribution is the same in each case. It is quite different, however, when the upstream flow rate is fixed, as in the experiments of Pedley & Stephanoff, because of differences in the undisturbed vorticity distribution, in the growth rate of the vorticity waves and in the dynamics of eddy A. A further finite-amplitude effect of importance, especially in an inviscid fluid, is the interaction of an eddy with its images in the channel walls.

Experimental data are presented that demonstrate the existence of a family of gravitational water waves that propagate practically without change of form on the surface of shallow water of uniform depth. The surface patterns of these waves are genuinely two-dimensional and fully periodic, i.e. they are periodic in two spatial directions and in time. The amplitudes of these waves need not be small; their form persists even up to breaking. The waves are easy to generate experimentally, and they are observed to propagate in a stable manner, even when perturbed significantly. The measured waves are described with reasonable accuracy by a family of exact solutions of the Kadomtsev-Petviashvili equation (KP solutions of genus 2) over the entire parameter range of the experiments, including waves well outside the putative range of validity of the KP equation. These genus-2 solutions of the KP equation may be viewed as two-dimensional generalizations of cnoidal waves.

A comparison of several commonly used turbulence models (including the K–ε model and three second-order closures) is made for the test problem of homogeneous turbulent shear flow in a rotating frame. The time evolution of the turbulent kinetic energy and dissipation rate is calculated for these models and comparisons are made with previously published experiments and numerical simulations. Particular emphasis is placed on examining the ability of each model to predict equilibrium states accurately for a range of the parameter Ω/S (the ratio of the rotation rate to the shear rate). It is found that none of the commonly used second-order closure models yield substantially improved predictions for the time evolution of the turbulent kinetic energy and dissipation rate over the somewhat defective results obtained from the simpler K–ε model for the unstable flow regime. There is also a problem with the equilibrium states predicted by the various models. For example, the K–ε model erroneously yields equilibrium states that are independent of Ω/S while the Launder, Reece & Rodi model and the Shih-Lumley model predict a flow relaminarization when Ω/S > 0.39 - a result that is contrary to numerical simulations and linear spectral analyses, which indicate flow instability for at least the range 0 [les ] Ω/S [les ] 0.5. The physical implications of the results obtained from the various turbulence models considered herein are discussed in detail along with proposals to remedy the deficiencies based on a dynamical systems approach.

The fluid dynamics associated with a compound drop consisting of a vapour bubble, partly surrounded by its own liquid in another immiscible liquid is considered. The fluid motion is analysed in the limit of Stokes flow and at the same time the surface tension forces are considered to be large enough to allow the interfaces to have uniform curvature. The flow field consists of translation and growth that can arise from change of phase.

An exact analytical solution for the axisymmetric flow field is obtained. The important results of physical interest are the drag force and the flow behaviour. In the case without growth, the drag force lies between the bubble and the solid-sphere limits for a sphere of the same volume as the total liquid and vapour dispersed phase. The maximum drag force is observed when the liquid and vapour volumes are nearly the same. This is the effect of weak circulation due to the smaller available space as compared with a spherical drop. With growth this effect appears to be enhanced. The flow streamlines exhibit secondary vortices in the dispersed phase when there is growth. The velocity field and the drag results here are applied to the heat transfer problem for the compound drop in Part 2 of this two-part series.

The present work is a comprehensive theoretical study of the heat transfer associated with a 3-singlet compound drop that is growing because of change of phase. The geometry is the same as in Part 1, i.e. a vapour bubble partially surrounded by its own liquid in another immiscible liquid. The attempt here is to gain fundamental understanding of the transport processes that take place in connection with direct-contact heat exchange. The fluid dynamics associated with its growth and translation is treated in Part 1. Here, that flow field solution is used to obtain the temperature field and hence the evaporation rate. The energy equation for the system consisting of a single compound drop is solved numerically by finite-difference methods. The results give the complete time history of evaporation of the drop. In addition, useful quantities such as the Nusselt number are given and compared with existing experimental data. Most of the results have good agreement with experimental data.