We first consider a steady laminar model of salt fingers and show that the latter become unstable with respect to internal gravity waves when the finger Reynolds number exceeds a critical value. The criterion is then used in speculations about the statistically steady state in a fully developed similarity model where horizontally averaged temperature and salinity gradients are constant at all depths. Dimensional reasoning is used to obtain the asymptotic dependence of the turbulent flux on the molecular salt diffusivity. From this and other relationships order-of-magnitude estimates are obtained and compared with laboratory experiments and ocean observations.

Experiments are presented in which axisymmetric internal waves are generated by an oscillating sphere moving vertically in a stably stratified salt solution. The Reynolds numbers for the sphere based on the diameter and the mean velocity are between 10 and 200. Lighthill's theory for dispersive waves is used to calculate the phase configuration of the internal waves. The agreement between experiment and theory is reasonably good.

Experiments on reverse transition were conducted in two-dimensional accelerated incompressible turbulent boundary layers. Mean velocity profiles, longitudinal velocity fluctuations $\tilde{u}^{\prime}(=(\overline{u^{\prime 2}})^{\frac{1}{2}})$ and the wall-shearing stress (TW) were measured. The mean velocity profiles show that the wall region adjusts itself to laminar conditions earlier than the outer region. During the reverse transition process, increases in the shape parameter (H) are accompanied by a decrease in the skin friction coefficient (Cf). Profiles of turbulent intensity (u’2) exhibit near similarity in the turbulence decay region. The breakdown of the law of the wall is characterized by the parameter \[ \Delta_p (=\nu[dP/dx]/\rho U^{*3}) = - 0.02, \] where U* is the friction velocity. Downstream of this region the decay of $\tilde{u}^{\prime}$ fluctuations occurred when the momentum thickness Reynolds number (R) decreased roughly below 400.

The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady temperature difference between the walls of the layer, a time-dependent sinusoidal perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The effects of the oscillating temperature field are treated by a perturbation expansion in powers of the amplitude of the applied field. The shift in the critical Rayleigh number is calculated as a function of frequency, and it is found that it is possible to advance or delay the onset of convection by time modulation of the wall temperatures.

A mechanism is proposed whereby planetary zonal flows can be generated by the resonant interaction of Rossby wave packets whose amplitudes are slowly varying functions of both space and time. Equations are derived describing the long-time behaviour of a resonantly interacting triad. At the first closure certain properties analogous to those already known for discrete waves are deduced. At the second closure, in the particular case when one of the members of the triad is a zonal flow, it is shown that the sideband resonance mechanism can cause energy to be gained or lost by this zonal flow. It is also shown that a single Rossby wave packet can exchange energy with a zonal flow with weak shear. In the final section a resonant quarter mechanism for producing zonal flows is discussed. A numerical estimate of the acceleration of a zonal current from a zero initial state gives values of a few km/day per day.

Measurements have been made of the wavelength of Taylor vortices between rotating cylinders. It is shown that the relaxation time of such a vortex system is approximately L2/6v, where L is the length of the vortex column and v is the kinematic viscosity. Previous measurements reported in the literature have not been steady-state measurements because of the long relaxation time. The present data are accurate to 1% and extend to 40 times the critical Taylor number. The variation of wavelength with Taylor number is linear and the slope is exceedingly small and negative. The non-uniqueness of wave-number observed by Coles (1965) in doubly periodic flows is here shown to occur in the rotationally symmetric case. It is argued that variational methods are inapplicable in determining the wave-number of finite-amplitude secondary flows. The experimental results show that the wave-number is determined uniquely by the initial conditions of the system. It is suggested that any method which neglects the time-dependent behaviour of the system cannot select the final state from the manifold of solutions which occur in non-linear problems.

The analysis of the sound field generated by the passage of isotropic turbulence through a shock of finite strength (Ribner 1953, 1954) has been extended to provide the flux of acoustic energy emanating from unit area on the downstream side of the shock. This is motivated by the problem of estimating the sound power emerging from a supersonic jet containing shock waves. The energy flux is found to vary almost linearly with shock density ratio, reaching a maximum at infinite Mach number of 0[sdot ]062 of the flux of turbulence kinetic energy convected into unit area of the shock.

Direct comparison with a result obtained by Lighthill (1953) is misleading. His energy relations, reckoned relative to a frame moving with the fluid, must be converted to the shock-fixed frame used herein. The converted results of his theory (weak shocks) and the results of our theory (arbitrary shocks) appear to show a similar asymptotic behaviour for vanishing shock strength; they diverge with increasing shock strength.

The effect of a streamwise pressure gradient on the velocity profile in the viscous sublayer of a turbulent flow along a smooth wall in two-dimensional flow is estimated. In the analysis, a similarity argument is used and the necessary empirical information obtained from a constant pressure flow. An allowance is made for the departure from the wall value of the gradient of total shear stress normal to the wall. The results of analysis were used to generate new additive constants for use with Townsend's modified law of the wall velocity profile and subsequently Townsend's profile is found to be in good agreement with the measured velocity profiles in an adverse pressure gradient.

When rotating Couette flow becomes unstable a periodic vortex structure is formed. For the wide-gap case, this flow is steady for a rather large range of the Taylor number above onset. In the region of finite amplitude instability the wave-numbers of the periodic structure are not unique. It is shown empirically that the non-uniqueness is not an end effect but a bonafide property of the flow and that the wave-form is a unique function of the wavelength. Data is presented to demonstrate the interval over which the wave-numbers can be varied when the parameters of the system are fixed. The large effect on the wave-form of small changes in the wavelength is also illustrated. These conclusions are based on extensive measurements of the azimuthal drift velocity for a particular mode of secondary flow.

Electrochemical techniques have been used to measure the velocity gradients at the surface of a cylinder for Reynolds numbers from 5 × 103 to 105. This is a companion study to that already reported by Dimopoulos & Hanratty (1968) for a Reynolds number range of 60–360. The use of a specially designed sandwich electrode enabled the direction of the velocity gradient as well as its magnitude to be measured. Of particular interest is the region of definite length after separation where the velocity gradient is negative, followed by an ill-defined region where the flow moves in the positive direction. Still farther downstream the direction of flow changes with time in an irregular fashion. The measured velocity gradients prior to separation are described satisfactorily by boundary-layer theory. The presence of a splitter plate in the rear of the cylinder eliminates periodic fluctuations in the wake and has a significant effect on the boundary layer prior to separation.

Finite difference solutions for the time dependent equations of motion have been carried out in order to extend the range of available data on steady flow around a cylinder to larger Reynolds numbers. At the termination of the calculations for R = 40 and 200, the separation angle, the drag coefficient and the pressure and vorticity distributions around the surface of the cylinder were very close to their steady-state values. For R = 500 the separation angle and drag coefficient were very close to their steady-state values but the pressure distribution and vorticity distribution at the rear of the cylinder were still changing slightly. The results at R = 500 were found to be quite different from those at R = 200 so it is not clear how closely we approximated the steady solution for R → ∞. The forces on the cylinder due to viscous drag and due to pressure drag are found to be smaller for steady flow than for laboratory experiments where the wake is unsteady.

It is shown that the criteria of Preston and of Patel & Head are special cases of a general Reynolds-number criterion which can be deduced as a requirement that there shall be some part of the boundary layer (in practice, the inner layer) in which the energy-containing and dissipating ranges of eddy size do not quite overlap.

The diffraction problem of a plane shock wave at the apex of an obtuse wedge treated by Lighthill (1950) is extended by assuming that the shock wave strikes the walls of the obtuse wedge at some finite oblique angle of incidence (not exceeding the critical angle). Transformations similar to that performed in the above-mentioned paper lead to a non-symmetrical boundary-value problem for an analytic function of a complex variable having a non-homogeneity in the form of a delta-function. It was found possible to extend, for the case considered, the method developed by Lighthill and construct the solution in almost as simple a form as given in the above-mentioned paper. The case of three-dimensional stationary flow is considered when the line of reflexion makes a finite angle with the edge of the wedge.

The measured pressure distributions over the front hemisphere of a hemispherecylinder combination placed in an aligned fields magneto-fluid dynamic flow are presented. Integration of the pressure profiles show that the form or pressure drag of the composite body first increases as the magnetic field strength increases, at a fixed flow velocity, but then decreases as the magnetic field becomes still stronger.