As a model for the erosion of a stably stratified fluid by an overlying turbulent region, the rate of advance of the mixing interface is calculated in terms of the probability distribution for eddies as a function of their size and velocity. Predicted rates of advance are then evaluated for two current models of intermittency in small-scale turbulence. Compared to available experimental data, one intermittency model, the β-model, is found to be in good agreement, while the other, the log-normal hypothesis, is discordant; unfortunately, the Reynolds number of the existing experiments is not large enough to yield a definitive test. At higher Re, similar experiments might be a useful complement to the alternative of measuring high-order moments. Some related experiments are suggested to test the model and measure the fractal dimension D.

The characteristics are studied of short surface waves superimposed upon, and interacting with, a long, finite-amplitude dominant wave of frequency N. An asymptotic analysis allows the numerical investigation of Longuet-Higgins (1978) to be extended to higher superharmonic perturbations, and it is found that, although they are distorted by the underlying finite-amplitude wave, gravity wavelets continue to propagate freely provided the dominant wave does not break. Capillary waves can, however, be blocked by short, steep, non-breaking gravity waves, so that in a wind-wave tank at short fetch and high wind speed, freely travelling gravity-capillary waves can be erased by the successive dominant wave crests.

A train or group of short gravity waves suffers modulations δk in its local wave-number because of the straining of the long wave, and large modulations Cδk in its apparent frequency measured at a fixed point (where C is the long wave phase speed), largely because of the Doppler shifting produced by the dominant wave orbital velocity. The spectral signatures of a wave train are calculated by stationary phase and are found to have maxima at the upper wavenumber or frequency in the range. If an ensemble of short-wave groups is sampled at a given frequency f at a fixed point, the signal is derived from groups with a range of intrinsic frequencies δ, but is dominated by those at the long-wave crest for which f = δ + k.u0, where u0 is the orbital velocity of the dominant wave. The apparent phase speed measured by a pair of such probes is the sum of the propagation speed c of the wavelet and the orbital velocity u0 of the long wave. When f/N is large, the apparent phase speed approaches u0, independent of f. These results are consistent with measurements by Ramamonjiarisoa & Giovanangeli (1978) and others in which the apparent phase speed at high frequencies is found to be independent of the frequency — the measurements do not therefore imply a lack of dispersion of short gravity waves on the ocean surface.

The eigenvalue problem for the ‘acoustic’ modes in an inviscid, perfect gas with a quiescent state of isothermal, uniform rotation in a circular cylinder is solved asymptotically for A2 ↑ ∞ with (γ — 1) A2 = O(1), where A is the peripheral Mach number and γ is the specific heat ratio. The limit (γ — 1) A2 ↓ 0 leads to a solution in terms of the confluent hypergeometric function for all A, and the resulting eigenvalue equation is solved explicitly for either A2 [lsim ] 1 or A2 [Gt ] 1. Attention is focused on those modes (likely to be of greatest practical importance) for which the peripheral speed of the wave relative to that of the container tends to the sonic speed as A2 ↑ ∞. Viscosity and heat conduction are significant in an inner domain of low density, wherein the solution is expressed in terms of a generalized hypergeometric function.

These exact solutions correspond to time-dependent motions in parabolic basins. A characteristic feature is that the shoreline is not fixed. It is free to move and must be determined as part of the solution. In general, the motion is oscillatory and has the appropriate small-amplitude limit. For the case in which the parabolic basin reduces to a flat plane, there is a solution for a flood wave. These solutions provide a valuable test for numerical models of inundating storm tides.

When a circular cylinder oscillates transversely in water at rest, a three-dimensional streaming flow streaked with the chains of separated dye sheets is produced over a certain range of amplitude of the oscillation. This paper reports observations of this three-dimensional flow instability.

The prediction of drag force on spheres whose diameters are comparable to or greater than the dimensions of jets to which they are exposed is found to be much more difficult than in the more usual ‘fully immersed’ cases. Experimental results show considerable scatter but prediction guidelines are given in the paper. In Reynolds-number terms all results are considered to be supercritical ones because of the typically very high turbulence intensities in the mixing regions of jets.