Steady finite amplitude two-dimensional solutions are obtained for the problem of convection in a horizontal fluid layer heated from below and rotating about its vertical axis. Rigid boundaries with prescribed constant temperatures are assumed and the solutions are obtained numerically by the Galerkin method. The existence of steady subcritical finite amplitude solutions is demonstrated for Prandtl numbers P < 1. A stability analysis of the finite amplitude solutions is performed by superimposing arbitrary three-dimensional disturbances. A strong reduction in the domain of stable rolls occurs as the rotation rate is increased. The reduction is most pronounced at low Prandtl numbers. The numerical analysis confirms the small amplitude results of Küppers & Lortz (1969) that all two-dimensional solutions become unstable when the dimensionless rotation rate Ω exceeds a value of about 27 at P ≃ ∞. A brief discussion is given of the three-dimensional time-dependent forms of convection which are realized at rotation rates exceeding the critical value.

The problem of the strong velocity disturbances remaining after the laminarization of an electroconductive fluid flow in a transverse magnetic field was investigated experimentally. The turbulence intensities, two-point correlations, and energy spectra of the velocity pulsations were measured using two-electrode probes and hot-film sensors. The two hypotheses with regard to a physical explanation of the persistence of the disturbances were examined, and it was concluded that these disturbances are generated mainly at the entry of the flow into the magnetic-field region. An almost undisturbed laminarized flow was obtained by eliminating the entry effects.

Experiments have been performed to determine the basic mechanism of heating in resonance tubes of square section with constant area excited by underexpanded jet flows. The jet flow between the nozzle exit and the tube inlet plays a key role in the performance of a resonance tube. A detailed and systematic investigation of the unsteady complex shock structure in this part of the flow region has led to a better understanding of the fundamental mechanisms associated with the gas heating in such tubes. A study of the effects of tube location in relation to free-jet shock location (without the presence of the resonance tube) has shed further light on the underlying mechanism of sustained oscillations of the flow in a resonance tube.

The far turbulent wake of a slightly heated cylinder was studied using our specially developed four-wire probe and digital processing of signals obtained. The processing method included a simultaneous solution of full nonlinear response equations for the four sensors yielding values of instantaneous velocity vector and temperature. The accuracy of results was improved substantially by the subtraction of free-stream velocity and temperature variations, first-order corrections for the d.c. drift of the signals, the elimination of 60 Hz related noise, and instantaneous correction for the streamwise displacement between the sensor wires. A low temperature threshold was used to discriminate between turbulent and potential flow.

The frequency of crossing of the turbulent-potential interface and statistics of turbulent and potential zone intervals are presented. Conditionally sampled fluctuating velocity and temperature fields are given for turbulent and potential zones as well as for a fluid at the downstream and upstream interface of the turbulent zones. Averaging was done with respect to conventional (Reynolds) as well as local zone or point means. The results on turbulence structure up to second-order correlations are presented in this paper.

It is hoped that the data will be useful for those interested in methods of prediction of turbulence, especially those based on the consideration of large structures. Researchers more interested in the physical phenomena involved might also find the data suitable for further analysis and interpretation.

Even very small Coriolis forces are shown to alter significantly the nature of the upstream wake of an object in slow (small Froude number) translation through a non-diffusive stratified fluid. If the Ekman number is of order one, the far upstream extent of the wake is reduced. If the fluid rotation is sufficient to make the Ekman number small, the contraction of the wake is much greater. We study a particular case in detail; the Ekman number is small enough to make horizontal boundary layers Ekman layers. In this case, the wake is confined to the vicinity of the object, the upstream flow arising from a combination of Ekman pumping and baroclinic vorticity generation. The upstream flow is described by an eigenfunction whose amplitude is dependent on object geometry. If the object is a semi-infinite rectangular parallelepiped, that amplitude is determined by detailed examination of the shear layer at the face of the parallelepiped and its interaction with the Ekman layer on the top surface of the object

This paper discusses the influence of turbulence convection on the formation of acoustic momentum and thermal boundary layers over a rigid surface in the presence of a low Mach number wall-turbulence shear flow. Equations which determine the modified boundary-layer profiles are obtained from a consideration of the relaxation of coherent perturbations in the Reynolds stress. These equations can be solved analytically for a wide range of conditions which are investigated in detail. The theory is applied to the problem of sound propagation in fully-developed turbulent pipe flow, and at low Mach numbers good agreement is obtained between predicted acoustic attenuation rates and experimental results available in the literature.

Recent measurements of the skewness of the derivative of the temperature fluctuation θ, implying the breakdown of local isotropy even in high Reynolds number shear flows, are examined. Using the temperature signal in a slightly heated axisymmetric jet, a detailed quantitative analysis is made of the suggestion that the observed presence of a well-defined large-scale pattern of the temperature signal in these flows is responsible for this breakdown. A selective ensemble averaging technique is used for separating this pattern from fluctuations superposed on it. The technique is extended to extract the large-scale patterns in simultaneously measured axial (u), radial (v) velocity fluctuations, and the products uv, uθ and vθ, so that it is possible to separate contributions of these patterns from those of the superposed fluctuations to several important turbulent quantities. The mean shape of the patterns, their degree of anisotropy and correlation, and their contribution to turbulence intensities and Reynolds shear stress are obtained. Probability densities and spectra of these quasi-homogeneous superposed fluctuations are also obtained. Results show that the fluctuations are consistent with local isotropy and make the dominant contribution to the turbulence intensities, that the large-scale patterns are responsible for the observed skewness values of the derivative of v, and that the fluctuations may be responsible for a significant part of the turbulent momentum and heat transport, especially in the region of the jet where the turbulent energy production is substantial.

A new integro-differential equation is derived for steady free-surface waves. Numerical solutions of this equation for periodic gravity-capillary waves on a fluid of infinite depth are presented. For the two limiting cases of gravity waves and capillary waves, our results are in excellent agreement with previous calculations. For gravity-capillary waves, detailed calculations are performed near the wave-number at which the classical second-order perturbation solution breaks down. Our calculations yield two solutions in this region, which in the limit of small amplitudes agree with the results obtained by Wilton in 1915; one solution has the small amplitude behaviour of a gravity wave and the other that of a capillary wave, but the numerical results show that at large amplitudes both waves have the characteristics of capillary waves. The calculations also show that the wavenumber range in which two solutions exist increases with increasing wave height.