A nonlinear integro-differential equation governing finite amplitude wave propagation on concentrated vortices is solved numerically. The solution to the Cauchy problem shows a solitary wave development qualitatively similar to solutions of the Korteweg–de Vries equation. A perturbation solution of the stationary form of the evolution equation confirms the unsteady calculation.

The convective motions in a rotating laterally-heated annulus have been studied experimentally. The main feature that differentiates this experiment from others done previously is a rigid lid which is in contact with the fluid. It has been found that the radial temperature differences at which the transition from lower symmetry to the vortex regime occur are different in the cases of positive and negative temperature gradients and that, in particular, the transition is a very strong function of Ω in the case of a negative temperature gradient. It has been observed further that the persisting vortices which form in the annulus always appear at the inner cylinder, whether the radial temperature difference is increased in a quasi-steady way, the radial temperature difference is applied suddenly while the mean temperature is maintained, the heating or cooling is applied suddenly on either the inner or outer cylinder only, thus changing the mean temperature, or whether the rotation of the annulus is started suddenly with the radial temperature difference applied beforehand. This is true regardless of whether the radial temperature gradient is positive or negative and there has not been a single instance in which a persisting vortex developed at the outer cylinder. Neither this observation nor the dependence of the transition temperature difference on Ω seems to be in agreement with the current theoretical descriptions of the annulus motions. On the other hand, the appearance of a warm cell, a counter cell and a cold cell in the time-dependent meridional motions observed in the experiments confirms the results of a numerical study of Williams (1967), which studies the symmetric motions in the annulus.

A wind-tunnel model was developed to study the two-dimensional turbulent boundary layer in adverse and favourable pressure gradients with out the effects of streamwise surface curvature. Experiments were performed at Mach 4 with an adiabatic wall, and mean flow measurements within the boundary layer were obtained. The data, when viewed in the velocity transformation suggested by Van Driest, show good general agreement with the composite boundary-layer profile developed for the low-speed turbulent boundary layer. Moreover, the pressure gradient parameter suggested by Alber & Coats was found to correlate the data with low-speed results.

This paper presents some new measurements which have been made on a drag-reducing polymer solution in pipe flow. A novel type of laser dopplermeter, which has been developed by the author, is briefly described and the measurements which have been obtained are given. These results and their implications are then discussed in terms of conventional models for turbulent flow in a pipe. These suggest that the polymer has very little effect upon the turbulent core of the flow, but thickens and stabilizes the viscous sublayer. The turbulent intensity inside the sublayer is unchanged but, owing to its thickening, the velocity fluctuations just outside are greater. There is not a general suppression of turbulence within the sublayer although well inside the sublayer the spanwise velocity component is found to be reduced.

A general method for studying two-dimensional problems in hydrodynamic stability is presented and applied to the classical problem of predicting instability in plane Poiseuille flow. The disturbance stream function is expanded in a Fourier series in the axial space dimension which, on substitution into the Navier-Stokes equation, leads to a system of parabolic partial differential equations in the coefficient functions. An efficient, stable and accurate numerical method is presented for solving these equations. It is demonstrated that the numerical process is capable of accurate reproduction of known results from the linear theory of hydrodynamic stability.

Disturbances that are stable according to linear theory are shown to become unstable with the addition of finite amplitude effects. This seems to be the first work of quantitative value for disturbances of moderate and larger amplitudes. A relationship between critical amplitude and Reynolds number is reported, the form of which indicates the existence of an absolute critical Reynolds number below which an arbitrary disturbance cannot be made unstable, no matter how large its initial amplitude. The critical curve shows significantly less effect of amplitude than do those obtained by earlier workers.

An infinitesimal centre disturbance is imposed on a fully Ldveloped plane Poiseuille flow at a Reynolds number R slightly greater than the critical value Rc for instability. After a long time, t, the disturbance consists of a modulated wave whose amplitude A is a slowly varying function of position and time. In an earlier paper (Stewartson & Stuart 1971) the parabolic differential equation satisfied by A for two-dimensional disturbances was found; the theory is here extended to three dimensions. Although the coefficients of the equation are coinples, a start is made on elucidating the properties of its solutions by assuming that these coefficients are real. It is then found numerically and confirmed analytically that, for a finite value of (R-Rc)t, the amplitude A develops an infinite peak at the wave centre. The possible relevance of this work to the phenomenon of transition is discussed.

Acoustic liners are often perforated screens backed by sound-absorbent material. Turbulence can interact with these screens to generate additional sound. The dynamics of the generation process is examined in this paper, where the liner is modelled as an infinite rigid plane boundary with a homogeneous array of circular orifices or rigid pistons. The acoustic properties of these boundaries are derived in the long wavelength limit. Small-scale turbulence is scattered by individual apertures into sound. Acoustically transparent surfaces support dipole scattering centres while more ‘opaque’ surfaces have monopoles at the apertures which convert turbulence into sound more effectively. It is shown that the process can be described once the response of an individual aperture in an infinite baffle is known. At low Mach numbers the screen can increase the sound radiated by adjacent turbulence by a factor equal to the inverse fourth power of the Mach number. Mean-flow effects are ignored but they are thought to increase the effects deduced in this preliminary study.

Simultaneous measurements of the sea surface displacement and the longitudinal component of the wind velocity at several levels are reported. They were obtained at the Marine Tower under various conditions, with the air and the waves moving either in the same or in opposite directions. The spectral analysis was made. The cross-correlation coefficient between the sea surface displacement and the wind velocity is large at the layer adjacent to the surface and decreases with increasing mean wind velocity and height. Below a certain level which is several times or several tens of times higher than the height of the critical level where the wind velocity component in the direction of wave propagation equals the wave velocity, the phase lag of the Fourier component of the wind velocity compared with the surface elevation component is about 160 to 190°. Above this layer the wave-induced wind component is very weak and the phase reversal takes place at the height where the mean wind velocity equals 1·2 to 1·5C, C being the phase velocity of wave. When the wind blows in the opposite direction from that of the wave propagation, the wind fluctuation is in phase with respect to the wave motion and the amplitude of wave-induced wind component is relatively large. Some discrepancies are shown between the observations and the predictions from the theory of inviscid fluids.

The local entrainment rate in the initial region of axisymmetric turbulent air jets has been measured by a novel method, which is an adaptation of the ‘porous-wall’ technique used by Ricou & Spalding (1961). The local entrainment rate, which is independent of the nozzle Reynolds number for values greater than 6 × 104, is strongly dependent upon the axial distance. At an axial distance of one nozzle diameter the local entrainment rate is only about one-third of that in the fully developed jet; the entrainment rate increases with increasing axial distance to reach the fully developed value at an axial distance of about thirteen nozzle diameters.