The properties of edge waves confined by the interaction of buoyancy and Coriolis forces to the vicinity of a rigid plane boundary in a rotating, stratified, electrically conducting fluid pervaded by a magnetic field are established in some simple cases. The background shear is taken to be zero, the basic Alfvén velocity V and Brunt–Väisälä frequency N are assumed uniform, and all dissipative effects are taken to be vanishingly small. It is shown that waves trapped against the bounding wall can occur only if V is parallel to the wall. When the basic rotation vector Ω is also parallel to the wall, the hydromagnetic edge waves have a higher frequency and smaller spatial extent perpendicular to the wall than their non-hydromagnetic counterparts, but more complex behaviour is found when Ω possesses a component normal to the wall. There are conditions under which edge waves may exist even when the basic density stratification is top-heavy (i.e. when N2 < 0).

The flow around a cylinder and a sphere rotating freely in a simple shear was studied experimentally for moderate values of the shear Reynolds number Re. For a freely rotating cylinder, the data were found to be consistent with the results obtained numerically by Kossack & Acrivos (1974), at least for Reynolds numbers up to about 10. Rates of rotation of a freely suspended sphere were also obtained over the same range of Reynolds numbers and showed that, with increasing Re, the dimensionless angular velocity does not decrease as fast for a sphere as it does for a cylinder. In both cases, photographs of the streamline patterns around the objects were consistent with this behaviour. Furthermore, it was found in each case that the asymptotic solutions for Re [Lt ] 1 derived by Robertson & Acrivos (1970) for a cylinder and by Lin, Peery & Schowalter (1970) for a sphere are not valid for Reynolds numbers greater than about 0.1, and that the flow remains steady only up to values of Re of about 6.

The initial flow field of an incompressible, viscous fluid around a circular cylinder, set impulsively to move normal to its axis, is studied in detail. The nonlinear vorticity equation is solved by the method of matched asymptotic expansions. Analytic solutions for the stream function in terms of exponential and error functions for the inner flow field, and of circular functions for the outer, are obtained to the third order, from which a uniformly valid composite solution is found. Also presented are the vorticity, pressure, separation point and drag. These quantities agree with the numerical computations of Collins & Dennis. Extended solutions developed by Padé approximants indicate that higher than third-order approximations will yield only minor improvements.

An attempt is made to explain theoretically two curious phenomena involving the motion of the liquid in a spinning, gyrating, liquid-filled gyroscope. One of the phenomena is the periodic breakdown of the free-surface wave form of the spinning liquid in the gyroscope when it gyrates at angles larger than about 1°. The other is the resonant amplitude growth rate of the liquid-filled gyroscope at these angles, for then the small angle stability theory of Stewartson (1959) fails to make the correct predictions.

The analysis exploits the experimental fact that the axis of rotation of liquid in the rotor of a spinning gyrating gyroscope does not remain coincident with the axis of rotation of the rotor when the gyroscope gyrates at amplitudes greater than the above-mentioned 1°. It is shown that this lack of coincidence generates Rossby waves and modifies the inertial wave frequencies that would ordinarily occur in a right circular cylinder. There is no nonlinear interaction between these Rossby and inertial waves; hence the free-surface breakdown remains unexplained. However, the modification of the inertial wave frequencies does seem to account for the curious amplitude growth rate.

The properties of reflexion, refraction and absorption of a gravity wave incident upon a shear layer are investigated. It is shown that one must expect these properties to be very different depending upon the parameters (such as the Richardson number Ri, the wavelength normalized by the length scale of the shear and the ratio of the flow speed to the phase speed of the wave) characterizing the interaction of a gravity wave with a shear layer. In particular, it is shown that for all Richardson numbers there is a discontinuity in the net wave-action flux across the critical level, i.e. at a height where the flow speed matches the horizontal phase speed of the wave. When Ri > ¼, this is accompanied by absorption of part of the energy of the incident wave into the mean flow. In addition it is shown that the phenomenon of wave amplification (over-reflexion) can arise provided that the ultimate shear flow speed exceeds the horizontal phase speed of the wave and Ri is less than a certain critical value Ric ≃ 0·1129, in which case the reflected wave extracts energy from the streaming motion. It is also pointed out that wave amplification can lead to instability if the boundary conditions are altered in such a way that the system can behave like an ‘amplifier’.

Measurements of higher-order spectra of turbulent velocity fluctuations in the atmospheric boundary layer over the open ocean and land produce the interesting result that, in the wavenumber range designated originally by Kolmogorov as an inertial subrange, the functional dependence of the spectra on wavenumber is practically independent of the order of the spectrum. These results confirm the observation of Dutton & Deaven that their extension by a dimensional similarity argument of the original Kolmogorov theory to higher-order spectra was not valid. In the present work, we derive an alternative generalization of the Kolmogorov ideas for spectra of arbitrary order. The results of this generalization describe the dependence upon wavenumber of the available data quite well. We also present theoretical calculations based on a Gaussian model for the fluctuating velocity field which furnish quantitative predictions for spectra of arbitrary order that are also in good agreement with the measurements, both in functional form and in absolute value.

Comparison of results based on the Gaussian model with laboratory measurements obtained in a free shear layer shows that the Gaussian theory predicts accurately all the available normalized higher-order spectra for all frequencies. When the corresponding measured higher-order moments are close to those expected for a Gaussian process, the Gaussian theory also correctly predicts the absolute magnitudes of the higher-order spectra.

The electron-beam fluorescence technique has been employed in measuring simultaneous density and temperature fluctuations in a hypersonic (M ≃ 16), adiabatic wall boundary layer. The paper discusses this technique, as it is applied to the conditions of relatively high density associated with turbulent flows. It presents general considerations concerning the attainable frequency response and spatial resolution of the technique. It describes results from initial measurements in a boundary layer on a wind-tunnel wall. These results show that the r.m.s. of the density, temperature and pressure fluctuations are large, much larger than observed in supersonic boundary layers.

We examine two-dimensional motion of a stably stratified fluid containing two solutes with different molecular diffusivities in an inclined slot. The two solutes have continuous opposing gradients with the slower-diffusing one more dense at the bottom. It is found that, in the steady state, there exists a slow upward flow along the slope driven by the slight buoyancy difference near the wall, not unlike the solution found by Phillips (1970) for a single solute. The magnitude of the flow is less than that in Phillips’ solution by a factor of approximately (1-λ)/(1-λτ), where λ is the ratio of the density gradient and τ−1 is the ratio of the diffusivity of the faster-diffusing solute to that of the slower-diffusing one. For the time-dependent flow resulting from switching on the diffusivities at t = 0, there may be a dramatic reversal of the flow near the walls depending on the relative magnitude of λ and τ. If λ is somewhat greater than τ, the initial flow is downward, along the slope, reaching a maximum magnitude about one order of magnitude greater than the steady-state value. Then the ‘reverse’ flow gradually diminishes and approaches the steady state rather slowly. For λ [gsim ] τ, the approach to the steady state is monotonic; there is no ‘reverse’ flow near the wall. The existence of the downward flow, which was observed by Turner & Chen (1974), may lead to double-diffusive instabilities which eventually result in horizontal convecting layers.

Stability experiments were made on plane Poiseuille flow generated in a long channel of a rectangular cross-section with a width-to-depth ratio of 27·4. By reducing the background turbulence down to a level of 0·05 %, we succeeded in maintaining the flow laminar at Reynolds numbers up to 8000, which is much larger than the critical Reynolds number of the linear theory, about 6000. The downstream development of the sinusoidal disturbance introduced by the vibrating ribbon technique was studied in detail at various frequencies in the range of Reynolds number from 3000 to 7500. This paper presents the experimental results and clarifies the linear stability, the nonlinear subcritical instability and the breakdown leading to the transition.

A similarity solution is obtained for a model of the turbulent starting plume comprising a steady plume feeding mass, momentum and buoyancy into a vortex ring. Bulk equations representing the time rate of increase of ring momentum and ring buoyancy, together with equations (dependent on broad features of the ring structure) representing the velocity of propagation and time rate of circulation increase are used to determine the motion of the vortex ring. The similarity solution is found to exist only for diffuse distributions of vorticity and buoyancy within the ring. Further, the ratio of ring velocity to plume velocity, which is assumed to be constant, is found to take a value which agrees with that obtained from experimental observations.

The way in which internal waves change in amplitude as they propagate through an incompressible fluid or an isothermal atmosphere is considered. A similarity solution for the small amplitude isolated viscous internal wave which is generated by a localized two-dimensional disturbance or energy source was given by Thomas & Stevenson (1972). It will be shown how summations or superpositions of this solution may be used to examine the behaviour of groups of internal waves. In particular the paper considers the waves produced by an infinite number of sources distributed in a horizontal plane such that they produce a sinusoidal velocity distribution. The results of this analysis lead to a new small perturbation solution of the linearized equations.

The bounded solution of the unsteady Stokes equations is obtained for the flow of a viscous incompressible fluid about a circular cylinder which undergoes a linear translation starting from rest. A drag formula which consists of the known added-mass term and an additional term arising from the presence of viscosity is obtained. The drag obtained is applied locally in a study of damped vibration of a string. It is shown that the usual theory based on the quasi-steady drag formula overestimates considerably the period and the decay rate of damped vibration of a string in a viscous fluid.