A two-dimensional stability analysis of the flow in a straight alluvial channel has been carried out, using the vorticity transport equation. In the analysis an attempt has been made to account for the influence of gravity on bed-load transport, and this turned out to change the stability quite significantly.

In the case of instability, the further growth of the dunes has been investigated using a second-order approximation, This nonlinear theory explains the experimental fact that the dunes very soon become asymmetric.

We consider the rapid rotation, in the sense of large Reynolds number ε−1, of a gravitating solid sphere in a monatomic gas. The flow is characterized by a thin boundary layer on the sphere and a thin, swirling, buoyant, radial jet in the equatorial plane. When the Prandtl number σ is of order unity, the boundary layer and jet are to first order uncoupled from the outer flow. For sufficiently small Prandtl number (which may be interpreted as approximating an optically thick radiating gas), the outer flow is boundary-layer driven. The parameter boundary between these two dissimilar steady states is σ = O(ε⅙).

In this paper an infinite waving sheet is used to model a micro-organism swimming either parallel to a single plane wall, or along a channel formed by two such walls. The sheet surface, which undergoes small amplitude waves, can represent either a single flagellum or the envelope of the tips of numerous cilia. Two different solutions of the equations of motion are presented, depending upon whether or not the wave amplitude is small compared with the separation distances between the sheet and walls. It is found that the velocity of propulsion is bounded by the velocity of wave propagation by the sheet. Both the propulsive velocity and rate of working by the sheet increase as the separation distances decrease. However, it is demonstrated that suitable alterations in wave speed or wave shape can fix the rate of working while still causing increases in propulsive velocity. Reductions in propagated wave speed, i.e. beat frequency, are particularly effective in this regard.

The properties of convective flow driven by an adverse temperature gradient in a fluid-filled porous medium are investigated. The Galerkin technique is used to treat the steady-state two-dimensional problem for Rayleigh numbers as large as ten times the critical value. The flow is found to look very much like ordinary Bénard convection, but the Nusselt number depends much more strongly on the Rayleigh number than in Bénard convection. The stability of the finite amplitude two-dimensional solutions is treated. At a given value of the Rayleigh number, stable two-dimensional flow is possible for a finite band of horizontal wavenumbers as long as the Rayleigh number is small enough. For Rayleigh numbers larger than about 380, however, no two-dimensional solutions are stable. Comparisons with previous theoretical and experimental work are given.

A linear stability analysis is applied to a stably stratified, thermally radiating shear layer. The grey Milne–Eddington approximation is employed as a radiation model. In contrast to a previously reported optically thin analysis, no inviscid instability exists, in the limit of vanishing horizontal wavenumber, for this selfabsorbing model. The inviscid neutral-stability boundary (Richardson number us. dimensionless wavenumber) for the Milne–Eddington approximation converges to the optically thick limit as the optical depth of the shear layer is increased. As the optical depth of the shear layer is decreased, the inviscid Milne–Eddington neutral-stability boundary approaches the optically thin limit, although not uniformly in the wavenumber. For fixed mean velocity gradient and fluid properties, the inviscid critical Richardson number approaches infinity as the optical depth of the shear layer approaches zero. Viscous effects neutralize this radiative destabilization, and the critical Richardson number eventually returns to zero as the optical depth continues to decrease. A shearlayer thickness exists for which the viscous critical Richardson number is a maximum. For shear depths greater than this thickness, self-absorption effects increase the stability; and for shear depths less than this thickness, viscous effects increase the stability. Results of the analysis are applied to the atmospheres of Venus and the earth. A critical Richardson number somewhat above the non-radiating value of 3 (although below the previously reported optically thin value) is found for the lower troposphere of the earth. No substantial effect is found for the earth's lower stratosphere or for the 100 km level above Venus.

An integral analysis of the type used to predict the flow of co-flowing jets has been applied to the problem of a sudden enlargement in a pipe (Borda–Carnot expansion). This technique successfully predicts all the overall flow parameters of interest (e.g. reattachment lengths, pressure profile, etc.). The analysis indicates that the downstream conditions (up to reattachment) are insensitive to wall shear and the point of minimum pressure does not coincide with the location of the maximum return-flow velocity.

In this paper, the change in energy dissipation due to a small hump on a body in a uniform steady flow is calculated. The result is used in conjunction with the variational methods of optimal control to obtain the optimality conditions for four minimum-drag problems of fluid mechanics. These conditions imply that the unit-area profile of smallest drag has a front end shaped like a wedge of angle 90°.

Flow visualization and laser-anemometry measurements are reported in the flow downstream of a plane 3: 1 symmetric expansion in a duct with an aspect ratio of 9·2: 1 downstream of the expansion. The flow was found to be markedly dependent on Reynolds number, and strongly three-dimensional even well away from the channel corners except at the lowest measurable velocities. The measurements at a Reynolds number of 56 indicated that the separation regions behind each step were of equal length. Symmetric velocity profiles existed from the expansion to a fully developed, parabolic profile far downstream, although there were substantial three-dimensional effects in the vicinity of the separation regions. The velocity profiles were in good agreement with those obtained by solving the two-dimensional momentum equation. At a Reynolds number of 114, the two separation regions were of different lengths, leading to asymmetric velocity profiles; three dimensional effects were much more pronounced. At a Reynolds number of 252, a third separation zone was found on one wall, downstream of the smaller of the two separation zones adjacent to the steps. As at the lower Reynolds numbers, the flow was very stable. At higher Reynolds numbers the flow became less stable and periodicity became increasingly important in the main stream; this was accompanied by a highly disturbed fluid motion in the separation zones, as the flow tended towards turbulence.

A turbulence representation, consisting of a generalized set of transport equations for the Reynolds stress tensor and the turbulence energy decay rate, is applied to the study of convective heat transport between parallel plates at moderate Rayleigh numbers, 5 × 103 ≤ Ra ≤ 6·4 × 105. A series of heat flux transitions, in good agreement with those observed experimentally, is detect, ed in this study and found to correlate with changes in the turbulence structure. In the order of increasing Rayleigh number these structural changes correspond to: the transition from laminar to turbulent flow, the transition from low to locally high intensity turbulence, the transition to uniformly high intensity turbulence, and the transition from a buoyancy dominated turbulence to a shear dominated turbulence. An analysis is made of the effect of each of these transitions on the mechanism for heat transfer between the plates.

A study has been made of the flow and disintegration of thin liquid sheets in combustion gases up to temperatures of 950°C. It is found that below 300°C sheet breakdown occurs through the growth of antisymmetric Kelvin–Helmholtz waves. Above this temperature high frequency symmetric waves and localized disturbances are superimposed on the sheet and disintegration then occurs by the combined action of aerodynamic waves and perforations, the contribution of the latter predominating with increasing temperature. It is demonstrated that the new wave system is electrohydrodynamic in origin, the electric field being generated by the charged species present in the gas. The drop size is found to be critically dependent upon the nature of the disintegration process.

An analytical study is made of simple models of steady fronts in the atmosphere in which the temperature field is subjected to deformation as the fluid moves downstream in a large-scale horizontal flow. One fundamental approximation is made and then a Lagrangian method, in which fluid particles are identified by conservation of entropy and potential vorticity, and by Bernoulli's theorem, enables the steady problem to be solved. Solutions for models of surface fronts and upper tropospheric fronts are compared with those obtained from a model in which there is no variation along the front and the frontogenesis proceeds in time. If the thermal wind is comparable with the basic wind, and the potential vorticity is not negligible in some sense, the frontogenesis is increased where the thermal wind opposes the basic flow but, decreased where it reinforces the flow.

Two-species, irreversible, very rapid reactions, with mild heat release, in a turbulent shear flow are shown to be analogous to the transport of two non-reacting species by the same shear field. Expressions for the probability density functions of the reacting species, the product species and the reaction-generated thermal field are obtained in terms of the joint probability density functions of the two nonreacting species. As an example we have constructed, from recent measurements of temperature statistics at a cross-section in a heated jet, the meanand fluctuating concentration fields of the reacting species and the mean concentration of the product.