Finite amplitude axisymmetric thermoconvective flows in a bounded cylindrical layer of fluid heated from beneath were calculated using Galerkin's method. Both systems with insulated and with conducting lateral boundaries were investigated for radius-to-depth ratios of 1, 2·25, 2·55 and 2·66. Flows bounded by a conducting lateral boundary were found to be unstable for Rayleigh numbers greater than 1·1 times the critical value. The cell size was found to be an increasing function of the Rayleigh number.

Convective flow of the cellular type has been investigated in vertical cylinders of axisymmetric and annular shape. The critical Rayleigh numbers were determined as functions of the box diameter and the gap width respectively. A distinct influence of side walls with different thermal conductivities was observed.

A European Mechanics Colloquium (Euromech 56) on ‘Nonlinear processes in rotating fluids’ was held at University College, London from 14–18 April 1975. It was attended by 77 mathematicians, engineers and physicists from 14 countries, and 33 papers were presented and discussed. The topics included motions in homogeneous and stratified rotating fluids, with applications to the atmosphere, the oceans, the earth's core and centrifuges. Brief summaries of the papers presented are contained in this report.

The paper describes an investigation of a subjectively distinguishable element of high speed jet noise known as ‘crackle’. ‘Crackle’ cannot be characterized by the normal spectral description of noise. It is shown to be due to intense spasmodic short-duration compressive elements of the wave form. These elements have low energy spread over a wide frequency range. The crackling of a large jet engine is caused by groups of sharp compressions in association with gradual expansions. The groups occur at random and persist for some 10−1s, each group containing about 10 compressions, typically of strength 5 × 10−3 atmos at a distance of 50 m. The skewness of the amplitude probability distribution of the recorded sound quantifies crackle, though the recording process probably changes the skewness level. Skewness values in excess of unity have been measured; noises with skewness less than 0·3 seem to be crackle free. Crackle is uninfluenced by the jet scale, but varies strongly with jet velocity and angular position. The jet temperature does not affect crackle, neither does combustion. Supersonic jets crackle strongly whether or not they are ideally expanded through convergent-divergent nozzles. Crackle is formed (we think) because of local shock formation due to nonlinear wave steepening at the source and not from long-term nonlinear propagation. Such long-term effects are important in flight, where they are additive. Some jet noise suppressors inhibit crackle.

A relation connecting the reflexion and transmission coefficients for scattering of water waves by a fixed body with the far-field radiated waves due to forced motions of the same body is derived. Two alternative derivations are given, including a simple argument based on the analysis of an appropriate linear superposition of the two problems, and a more formal application of Green's theorem to the two potentials. For bodies with horizontal symmetry, the transmission and reflexion coefficients are related to the phase angles of the far-field radiated waves associated with symmetric and antisymmetric forced motions of the body. Some general conclusions follow for arbitrary symmetric bodies, and these are verified in specific cases by comparison with existing solutions. The applicability of these relations to other types of wave problem is noted.

The flow near the bow of a steadily turning ship is analysed using a modified slender-body theory. The rate of change of flow quantities in the longitudinal (x) direction is assumed to be greater than that implied by ‘conventional’ slender-body theory. As a consequence some features of high Froude number flow are apparent which cannot be predicted by the ‘conventional’ theory. The modified slender-body theory proposed requires the solution of a two-dimensional Laplace equation (in y and z) but its free-surface condition still involves an x derivative. A Fourier-transform method is used to solve this problem. A simple bow configuration of constant draft is analysed and numerical results for the free-surface elevation are presented.

A Mach-Zehnder interferometer was used to study the interaction between convection currents in the sea water and the ice-water interface during freezing. The temperature at the ice-water interface during the early stages of freezing was approximately 0 °C, not the equilibrium freezing temperature. Salt plumes were observed to appear first at specific sites on the ice-water interface. This is contrary to earlier results reported by Farhadieh & Tankin (1972). The salinity profiles in the salt plumes were measured using interferograms in conjunction with Abel inversion. The maximum salinity, along the centre-line of the salt plume, is an indication of the salinity of the brine trapped within the ice.

The linear stability of a shear layer of an inviscid compressible fluid is considered. It is shown that there is instability of two-dimensional disturbances at all values of the Mach number, contrary to previous results for a vortex sheet. The difference arises from the discovery of a second unstable mode. This mode is supersonic, decays weakly with distance from the shear layer, and is not governed by the principle of exchange of stabilities. Detailed numerical and asymptotic results are given for the hyperbolic-tangent shear layer.

This paper reports measurements of turbulent quantities in an axisymmetric wall jet subjected to an adverse pressure gradient in a conical diffuser, in such a way that a suitably defined pressure-gradient parameter is everywhere small. Self-similarity is observed in the mean velocity profile, as well as the profiles of many turbulent quantities at sufficiently large distances from the injection slot. Autocorrelation measurements indicate that, in the region of turbulent production, the time scale of ν fluctuations is very much smaller than the time scale of u fluctuations. Based on the data on these time scales, a possible model is proposed for the Reynolds stress. One-dimensional energy spectra are obtained for the u, v and w components at several points in the wall jet. It is found that self-similarity is exhibited by the one-dimensional wavenumber spectrum of $\overline{q^2}(=\overline{u^2}+\overline{v^2}+\overline{w^2})$, if the half-width of the wall jet and the local mean velocity are used for forming the non-dimensional wavenumber. Both the autocorrelation curves and the spectra indicate the existence of periodicity in the flow. The rate of dissipation of turbulent energy is estimated from the $\overline{q^2}$ spectra, using a slightly modified version of a previously suggested method.

Supercavitating hydrofoils of large aspect ratio operating near a free surface are investigated, assuming an inviscid and irrotational flow with the effects of gravity and surface tension neglected. The flow near the foil, treated as two-dimensional, is solved by a nonlinear free-streamline theory, then a three-dimensional ‘downwash’ correction is made using Prandtl's lifting-line theory. The strength of the lifting-line vortex is determined by information from the two-dimensional solution through a matching procedure, in which the inverse of aspect ratio is used as a small parameter for asymptotic expansions. The analysis incorporates a free-surface reference level to determine the submergence depth of the foil. The present method can be applied to any type of foil having an arbitrary planform or profile shape, including a rounded leading edge, a twist and even a small dihedral angle, within the assumption of large aspect ratio. Numerical computations made on rectangular flat-plate hydrofoils show excellent agreement of results with existing experimental data, even for large angles of attack and relatively low aspect ratios. The pressure distributions, shapes of the cavity and free surface are also calculated as a function of spanwise position.

The creeping motion through a circular tube of neutrally buoyant Newtonian drops which have an undeformed radius comparable to that of the tube was studied experimentally. Both a Newtonian and a viscoelastic suspending fluid were used in order to determine the influence of viscoelasticity. The extra pressure drop owing to the presence of the suspended drops, the shape and velocity of the drops, and the streamlines of the flow are reported for various viscosity ratios, total flow rates and drop sizes.

In this paper two aspects of the deepening of a mixed layer in a stratified fluid are examined in the laboratory. The first is the deepening of a layer into a region of constant density gradient. Turbulence is produced by an oscillating grid which generates a horizontally homogeneous field of motion with no significant mean flow. It is found that the rate at which the potential energy of the basic stratification is increased by the mixing does not bear a simple relationship to the rate of energy input by the grid. On the other hand, when allowance is made for the decay of turbulent energy away from the grid and only that portion to reach the bottom of the mixed layer is considered, the rate of potential energy increase is found to be proportional to this available energy. The second aspect to be discussed is the effect of energy radiation by internal waves in the region below the mixed layer. Estimates are made of the possible loss of energy to these waves, which reduces the amount available to deepen the layer. An experimental demonstration of up to 50 % reduction in the mixing rate due to the presence of internal waves is given. Finally, the implications of these results are discussed in the light of current theoretical models of the deepening process.

The influence of a mean uniform shear on the development of a partially mixed region in an unbounded stratified fluid is considered. Results are given for the very near field and the far field in the large-J (Richardson number) limit. A qualitative discussion for J [gsim ] 1 is also included. The near-field motion is modified on a time scale given by Rτ ∼ J−¼, where R = dU/dz is the mean shear strength. This modification is shown to be a consequence of the kinematic distortion of the wake profile by the mean shear. The radiation field is largely anticipated by the wave-packet discussion of an earlier paper.