The mean flow development in an initially turbulent boundary layer subjected to a large favourable pressure gradient beginning at a point x0 is examined through analyses expected a priori to be valid on either side of relaminarization. The ‘quasi-laminar’ flow in the later stages of reversion, where the Reynolds stresses have by definition no significant effect on the mean flow, is described by an asymptotic theory constructed for large values of a pressure-gradient parameter Λ, scaled on a characteristic Reynolds stress gradient. The limiting flow consists of an inner laminar boundary layer and a matching inviscid (but rotational) outer layer. There is consequently no entrainment to lowest order in Λ−1, and the boundary layer thins down to conserve outer vorticity. In fact, the predictions of the theory for the common measures of boundary-layer thickness are in excellent agreement with experimental results, almost all the way from x0. On the other hand the development of wall parameters like the skin friction suggests the presence of a short bubble-shaped reverse-transitional region on the wall, where neither turbulent nor quasi-laminar calculations are valid. The random velocity fluctuations inherited from the original turbulence decay with distance, in the inner layer, according to inverse-power laws characteristic of quasi-steady perturbations on a laminar flow. In the outer layer, there is evidence that the dominant physical mechanism is a rapid distortion of the turbulence, with viscous and inertia forces playing a secondary role. All the observations available suggest that final retransition to turbulence quickly follows the onset of instability in the inner layer.

It is concluded that reversion in highly accelerated flows is essentially due to domination of pressure forces over the slowly responding Reynolds stresses in an originally turbulent flow, accompanied by the generation of a new laminar boundary layer stabilized by the favourable pressure gradient.

Thin viscous jets are considered as they slowly fall, in a state of near-neutral buoyancy, through a liquid. An equation is derived which describes the path of the jet. A small perturbation analysis of nearly vertical jets is carried out, and shows that they are necessarily unstable and will eventually deviate significantly from the vertical. Numerical integration of the nonlinear equation describes the nature of this deviation. These results model some experimental observations made by Taylor (1969).

The internal waves produced by a moving body are generally longer in the direction of motion than the corresponding surface waves. This difference is accentuated when the density variation is slight and the body velocity is large in which case a very long towing tank may be required for the simulation of a steady-state condition. The following theoretical study of transient waves is intended as a step in relating test conditions and requisite towing-tank sizes.

A source–sink pair travelling for a finite time is used to represent the restricted motion of a body in a tank. The approximate length and volume of the body are fixed, but its precise shape (somewhat irregular and slightly time dependent) is assumed to be of secondary importance and is not calculated here. The density-stratified fluid is assumed to have a constant Brunt–Väisälä frequency.

A solution in the form of a triple sum over the tank eigenfunctions applies quite generally for the internal wave system (neglecting surface waves and the potential-flow-type solution near the body). Examples covering the large-scale structure of the flow field have been solved for two values of an approximate similarity parameter. The value of the similarity parameter indicates how closely steady-state conditions are approached. The first (larger) value chosen produces a well-defined quasi-steady state near the body with transient fluctuations of the order of ± 10%. The second (smaller) value gives a poorly defined quasisteady state with fluctuations of the order of ±50%. More elaborate studies varying the tank length, width and depth could be made by programming the calculations.

The effect of a collapsing wake has not been considered here, but might possibly be treated by similar methods.

An analysis is made of the flow within a three-dimensional explosion, or spark, created in a gas absorbing energy from a steady conical beam of radiation with nearly spherical symmetry. The radiation, typically from an array of lasers with a common focus, is assumed to be very intense, and absorbed immediately behind an outwardly advancing strong shock. The resulting self-similar flow has previously been studied for spherical symmetry; somewhat improved calculations for that case are presented here.

Departures of the laser power from spherical uniformity, which would result from practical problems of arrangement, are conveniently represented by an ascending series of Legendre polynomials in the polar angle. For non-uniformities of small amplitude, first-order perturbations of the flow field are analysed in detail. Self-similarity is shown to be retained, for zero counter-pressure and power constant with time.

For the first five harmonics in power distortion, the resulting fourth-order system of equations is solved numerically for profiles of velocity components, density and pressure, and for shock shape. Results are presented graphically. These solutions are singular near the focus, but are nevertheless fully determined. In the limit of large wavenumber, the core of the flow has vanishing tangential velocity and pressure perturbations, and hence the governing equations are only of second order, except presumably in a boundary layer appearing near the shock.

Study of the nonlinear case of large wavenumber along the axis of symmetry shows that the singularity at the focus reflects the existence of a ‘forbidden zone’ whose extent depends on the degree of asymmetry. It is argued that this zone is one within which diffusional processes must dominate.

This paper describes how the flows around two circular cylinders, displaced in a plane normal to the free stream, interact as the two bodies are brought close together. Surface pressure measurements at a Reynolds number of 2·5 × 104, based on the diameter of a single cylinder, show the presence of a mean repulsive force between the cylinders. An instability of the flow was found when the gap between the cylinders was in the range between one diameter and about 0·1 of a diameter. Correlation measurements of hot-wire outputs indicate how mutual interference influences the formation of vortex streets from the two cylinders. Spanwise correlation measurements show that the correlation length doubles as the cylinders are brought into contact.

The outer region of a turbulent boundary layer along a flat plate was photographed and analysed; in addition, limited observations of the wall area were also made. The technique involved suspending very small solid particles in water and photographing their motion with a high-speed camera moving with the flow.

The single most important event observed in the outer region was fluid motion which in the convected view of the travelling camera appeared as a transverse vortex. This was a large-scale motion transported downstream almost parallel to the wall with an average velocity slightly smaller than the local mean. It appeared to be the result of an instability interaction between accelerated and decelerated fluid, and it is believed to be closely associated with the wall-region ejections. The transverse vortex was part of a deterministic sequence of events; although these events occurred randomly in space and time. The first of these events was a decelerated flow exhibiting velocities considerably smaller than the local mean. It was immediately followed by an accelerated flow. Both these events extended from near the wall to the far outer region. Their interaction resulted in the formation of one or more transverse vortices. While the transverse vortex was transported downstream, small-scale fluid elements, originating in the wall area of the decelerated flow, were ejected outwards (ejection event). After travelling some distance outwards the ejected elements interacted with the oncoming accelerated fluid in the wall region and were subsequently swept downstream (sweep event). The sequence of events closed with two large-scale motions.

Estimated positive and negative contributions to the instantaneous Reynolds stress during the events were many times higher than the local mean values.

An analysis is presented of the motion of a turbulent thermal in an unstratified environment. Although based upon the entrainment hypothesis introduced by G. I. Taylor (see Morton, Taylor & Turner 1956), the analysis differs from previous work in that it is not limited to small density differences between the thermal and its surroundings. Also, the influence of the virtual mass of the unsteadily moving fluid, ignored by previous investigators, is included and shown to be of significance for any density difference.

Calculations of the temporal variations of size, velocity and density are presented in non-dimensional form for thermals with initial density ratios covering the practically attainable range. It is shown a posteriori that losses of momentum and buoyancy to a wake are probably of negligible influence in any real case.

Convection in water above ice penetrates into the stably stratified region above the density maximum at 4 °C. Two-dimensional penetrative convection in a Boussinesq fluid confined between free boundaries has been studied in a series of numerical experiments. These included cases with a constant temperature at both boundaries as well as cases with a fixed average flux at the lower boundary. Steady convection occurs at Rayleigh numbers below the critical value predicted by linear theory. At high Rayleigh numbers, resonant coupling between convection and gravitational modes in the stable layer excites finite amplitude oscillations. The problem can be described by a simplified model which allows for distortion of the mean temperature profile and balances the convected and conducted flux. This model explains the finite amplitude instability and predicts the Nusselt number as a function of Rayleigh number. These predictions are in excellent agreement with the computed results.

The object is to predict the nature of small-amplitude long-period oscillations of a homogeneous rotating fluid over a ‘sea bed’ that is nowhere level. Analytically, we are limited to special choices of bottom topography, such as sinusoidal corrugations or an undulating continental slope, so long as the topographic restoring effect equals or exceeds that due to planetary curvature (the beta-effect). (Very slight topographic features, on the other hand, provide weak, resonant interactions between Rossby waves.)

Integral properties of the equations, and computer experiments reported elsewhere, verify the following results found in the analytical models: typical frequencies of oscillation are [lsim ]fδ, where f is the Coriolis frequency and δ measures the fractional height of the bottom bumps; an initially imposed flow pattern of large scale will rapidly shrink in scale over severe roughness (even the simplest analytical model shows this rapid change in spatial structure with time); and energy propagation can be severely reduced by roughness of the medium, the energy velocity being of order fδa, where a is the horizontal topographic scale (although in an exceptional case, the sinusoidal bottom, the group velocity remains finite for vanishingly small values of a).

We examine the hydromagnetic stability of a radially stratified fluid rotating between two coaxial cylinders, with particular emphasis on the case when the angular velocity greatly exceeds both buoyant and Alfvén frequencies. If the magnetic field is predominantly azimuthal instabilities then have an essentially non-axisymmetric and wavelike character. Various bounds on their phase speeds and growth rates are derived, including a ‘quadrant’ theorem analogous to Howard's semicircle theorem for Kelvin–Helmholtz instability. Their strong tendency to propagate against the basic rotation (i.e. ‘westward’), previously noted by the author in the study of a more simplified (homogeneous) model, seems relatively insensitive to the generation mechanism (e.g. unstable gradient of magnetic field, angular velocity or density), but a number of counterexamples show that this constraint need not apply if the magnetic field displays significant spatial variations of direction as well as magnitude and that eastward-propagating amplifying modes are then possible.