The properties of high frequency capillary waves generated by steep gravity waves on deep water have been measured with a high resolution laser optical slope gauge. The results have been compared with the steady theory of Longuet-Higgins (1963). Good qualitative agreement is obtained. However, the quantitative predictions of the capillary wave slopes cannot be verified by the data because the theory requires knowledge of an idealized quantity - the crest curvature of the gravity wave in the absence of surface tension - which cannot be measured experimentally.

Using a two-layer fluid model, equations are developed which describe long internal waves propagating along a channel of arbitrary cross-section. Expressions for the phase speed of these waves are derived in terms of geometric properties of the cross-section. When weakly nonlinear effects are balanced by weak dispersion, a Korteweg-de Vries equation is derived to describe the waves. The effects of a slowly varying cross-section are included. Applications of the theory are made to recent observations of internal surges in lakes.

Thermal convection in a fluid contained between two rigid walls with different mean temperatures is considered when either spatially periodic temperatures are prescribed at the walls or surface corrugations exist. The amplitudes of the spatial non-uniformities are assumed to be small, and the wavelength is set equal to the critical wavelength for the onset of Rayleigh-Bénard convection. For values of the mean Rayleigh number below the classical critical value, the mean Nusselt number and the mean flow are found as functions of Rayleigh number, Prandtl number, and modulation amplitude. For values of the Rayleigh number close to the classical critical value, the effects of the non-uniformities are greatly amplified, and the amplitude of convection is then governed by a cubic equation. This equation yields three supercritical states, but only the state linked to a subcritical state is found to be stable.

It is shown that the wavelets which appear on the inertial wave form of the inner free surface of a fully spun-up cylindrical mass of liquid contained in a vertical, rapidly rotating and gyrating gyrostat are capillary waves. It is further shown that the interaction between these capillary waves and the excited inertial waves is not the mechanism which effects an observed two-period collapse (‘breakdown’) and reappearance of the free-surface inertial wave form. Rather, the two-period breakdown can be explained by the conjecture that it is a beat phenomenon arising from the interaction of two differently structured inertial wave modes, which have the same frequency at small amplitudes of oscillation of the gyrostat but which, owing to the dependence of the inertial mode frequency on the amplitude of the gyrostatic motion, have slightly different frequencies at larger amplitudes of oscillation of the gyrostat.

Two similar problems are considered: what is the effect of applying a uniform and constant rate of strain (i) to the two-dimensional thermal mixing region in a homogeneous grid-generated turbulent field, and (ii) to the two-dimensional velocity mixing region formed between two uniform streams moving with different mean velocities? The imposed strain field is orientated so as to compress or separate the isothermal and isokinetic surfaces in the plane of interest.

Two theoretical models are presented; in the first, the profiles of temperature and velocity are assumed to be self-preserving and an assumption is made about the velocity scales; in the second, the statistical, rapid-distortion approach to dispersion due to Hunt & Mulhearn (1973) is applied. The circumstances in which these models differ and those where the simpler self-preserving model can be applied are determined. The measurements presented here indicate that the widths of both mixing layers decrease within the strain field, the width of the thermal mixing layer decreasing at a greater rate than that of the velocity mixing layer. However, the measured length scales were found to be 5% larger than the scales predicted by either of the analyses, which differed from each other by 5%. It is suggested that selective amplification of the energy-containing eddies by the strain field is responsible.

Proposals are made for modelling the pressure-containing correlations which appear in the transport equations for Reynolds stress and heat flux in a simple way which accounts for gravitational effects and the modification of the fluctuating pressure field by the presence of a wall. The predicted changes in structure are shown to agree with Young's (1975) measurements in a free stratified shear flow and with the Kansas data on the atmospheric surface layer.

Turbulence produced by a grid which simultaneously imparts a mean temperature profile varying linearly with height was investigated in a specially constructed wind tunnel. While the mean temperature profile is preserved downstream of the grid in accordance with the theory of Corrsin (1952), the downstream evolution of the r.m.s. temperature fluctuation is at variance with his prediction. The reason for this discrepancy is shown to lie in the neglect of molecular diffusivity, which leads to unbounded growth of the fluctuations. Along with conventional correlations and spectra, the filtered heat-transfer correlation is presented. About 60% of the heat transport is accomplished by the low wavenumber components having length scales equal to or larger than the integral scale. An intriguing feature of the present experiments is the presence of an inertial-convective subrange for the temperature field notwithstanding the low Reynolds number and the consequent absence of an inertial subrange for the velocity field. Experimental results show that the temperature has a positive skewness everywhere in contrast to the velocity components, which are symmetrically distributed. Measurements of the joint probability density function of the vertical component of the velocity and the temperature indicate that, while the assumption of joint normality is not uniformly valid, the conditional expectations nearly follow the normal law. Marginal and joint moments of up to fourth order are presented. Odd-order joint moments are clearly sensitive to the skewness of the temperature.

Measurements have been made in a water channel of the flow in and around the separation region due to a rearward-facing step. Detailed profiles of mean velocities, turbulence intensities and Reynolds shear stress are presented. The turbulence measurements reveal the development of a new shear layer, which splits at reattachment with about one-sixth of the mass flow deflected upstream. The new shear layer is associated with a region of roughly constant values of both the non-dimensional mixing length l/x and the shear correlation coefficient K. The mixing-length ratio is larger than that found in plane mixing layers, whereas the shear coefficient is roughly the same. There is strong evidence that near the wall the length scales increase more rapidly with distance from the wall than in an attached boundary layer, and that a local maximum occurs.

A Navier-Stokes direct spectral simulation code was modified to produce stationary and nearly isotropic turbulence in three dimensions. An approximate $-\frac{5}{3}$ energy spectrum was maintained over the entire range of wavenumbers by simultaneously driving the fluid and supplementing the ordinary viscosity with a subgrid-like energy sink in the last 15% of the spectrum. Half-tone and contour plots of the fluctuations in the vorticity, rate-of-strain tensor and helicity show increasing ‘spottiness’ as the system evolves in time. Probability distributions and cross-correlations among these three quantities were also obtained. The flatness factor of the longitudinal velocity derivative, the longitudinal structure functions and the fluctuations in the locally averaged dissipation rate are consistent with some degree of intermittency, but do not unambiguously demonstrate its presence in the simulated flows.

The following problem is treated: given a plane acoustic wave propagating through an unbounded field of turbulence, calculate the amount of acoustic energy converted into turbulent kinetic energy. The fluid velocities due to the acoustic waves and the turbulence are assumed to be small compared with the speed of sound. Thus the sound-turbulence interaction is weak and the turbulent field may be considered to be incompressible. The analysis is based on the interaction of two opposite effects: the acoustic distortion of the turbulence (producing anisotropic Reynolds stresses) and the redistribution of the kinetic energy among components (tendency towards isotropy) and among wavenumbers (energy cascade and dissipation). These phenomena are described using semi-empirical turbulence arguments. It is seen that the simplest model for the redistribution among components is not sufficient for unsteady flows. A more complete model is used which is modified to agree with the exact instantaneous distortion analysis of Ribner [map ] Tucker to first order. Owing to the two redistribution effects, the Reynolds stress behaves inelastically and is out of phase with the acoustic field. Thus there is an average production of turbulent energy corresponding to the absorption of acoustic energy and attenuation of the incident wave. For nearly isotropic turbulence, the attenuation coefficient is found to be proportional to the rate of viscous dissipation and independent of the frequency.

In order to compare the theory with experiment several constants involved in the semi-empirical model of the turbulence must be found. Owing to the lack of better information these constants are estimated here by order-of-magnitude considerations. No existing experiments correspond to the homogeneous turbulence assumed by the theory. Comparison with the few reasonably applicable experiments shows qualitative agreement though the importance of the turbulent absorption is generally of nearly the same order as the measurement error. Several discrepancies between jet noise experiments and aerodynamic noise predictions may be roughly explained using the above analysis.