The paper deals with an extension of previous work on the radiation properties of turbulent flow formed on compliant surfaces. The effect of simple supports is shown to be acoustically equivalent to an extended dipole system of strength equal to the support stress. The dipole radiation is reduced by a transmission factor below that radiated into a uniform environment. A particular example is worked out in detail. That example deals with the case of a single point support on an otherwise homogeneous surface excited by boundary-layer turbulence.

The development of waves and currents resulting from the action of a steady wind on initially standing water has been investigated in a wind–water tunnel. The mean air flow near the water surface, the properties of wind waves, and the drift currents were measured as they evolved with increasing fetch, depth and mean wind speed. The results suggest how the stress on the water surface changes with an increasingly wavy surface, and, from a different viewpoint, how the drift current and the waves develop in relation to the friction velocity of the air. The amplitude spectra calculated for the wavy surface reflected certain features characteristic of an equilibrium configuration, especially in the higher frequencies. The observed equilibrium range in the high frequencies of the spectra fits the f−5 rule satisfactorily up to frequencies f of about 15 c/s. The wave spectra also revealed how the waves grow in the channel, both with time at a fixed point, and with distance from the leading edge of the water. These results are discussed in the light of recent theories for wave generation resulting from the action of pressure fluctuations in the air, and from shearing flow instabilities near the wavy surface. The experimental observations agree reasonably well with the predictions of the recent theory proposed by Miles, using growth rates calculated for the mechanism suggesting energy transfer to the water through the viscous layer in the air near the water surface.

A considerable quantity of observations and measurements exists concerning the phenomenon of intermittency which is connected closely with the entrainment process in free turbulent flows. A number of these are described in the first part of the paper and conclusions are drawn about the shape and motion of the bounding surface that separates turbulent and non-turbulent fluid. The salient features are that indentations of the surface grow and decay cyclically, that each cycle leads to substantial entrainment of ambient fluid into the turbulent region, that the indentations move at a considerable speed relative to the free stream, and that the surface has a comparatively simple form. The growth–decay cycle of the indentations suggests that a critical condition for growth exists, but the pressure field consequent on the convection velocity of the indentations makes for a Helmholtz type of instability that is unlikely to be stabilized by purely viscous behaviour of the turbulent fluid. It is known that the initial response of turbulent fluid to distortion is elastic in character, with incremental Reynolds stress proportional to increment of total strain, and sufficient rigidity could stabilize the bounding surface. A simple flow model–an inviscid stream flowing over an elastic jelly—is examined and the condition for marginal stability is compared with the observed properties of the flow. The model leads to the conclusion that indentations of more than a critical wave-number are stable, and provides reasons for the comparatively simple form of the surface and for the occurrence of indentations in groups of about three. The relative values of entrainment constants in different flows of uniform density do not depend critically on the nature of the entrainment process provided that the main turbulent motion remains geometrically similar, but the correlation between entrainment constant and relative depth of the indentations found by Gartshore (1966) appears as a consequence of the ‘elastic’ control of the growth–decay cycle. Lastly, the properties of the engulfment mechanism are used to show that the entrainment constant for a jet is proportional to the square root of the ratio of ambient density to the average density inside the jet. In contrast, the corresponding result for engulfment controlled by an eddy viscosity is variation as the ratio of the mean of the ambient and inside density to the inside density. Observations of high-speed jets of water in air and air in water give some support to the ‘elastic’ hypothesis.

A general theory is presented to account for the small, free, lateral motions of a flexible, slender, cylindrical body immersed in fluid flowing parallel to the position of rest of its axis. The cylinder is either clamped or pinned at both ends, or clamped at the upstream end and free at the other; it lies in a horizontal plane wherein all motion is considered to be confined. It is shown that for sufficiently large flow velocities the cylinder may be subject to buckling and oscillatory instabilities in its first and higher flexural modes, respectively. It is shown that for cylinders with both ends supported the oscillatory instabilities are specifically caused by lateral frictional forces, and that in the absence of hydrodynamic-drag effects only buckling is possible. The same applies for cylinders supported at the upstream end and with a very long, gradually tapering free end. The critical conditions of stability, expressed in dimensionless form, are evaluated extensively for clamped-free and pinned-pinned cylinders, illustrating the effect of the various system parameters on stability.

The experiments described here were designed to illustrate the dynamical behaviour of flexible cylinders in axial flow theoretically examined in Part 1. Rubber cylinders, either clamped or pinned at the upstream end and free at the other, or pinned at both ends, displayed both buckling and oscillatory instabilities when immersed in flowing water of sufficiently high velocity. The conditions of neutral stability were determined in a number of cases and compared with theory. The observations were in substantial agreement with the theory.

This paper elaborates on the assertion that energy methods provide an always mathematically rigorous and a sometimes physically precise theory of sub-critical convective instability. The general theory, without explicit solutions, is used to deduce that the critical Rayleigh number is a monotonically increasing function of the Nusselt number, that this increase is very slow if the Nusselt number is large, and that a fluid layer heated from below and internally is definitely stable when $RA < \widetilde{RA}(N_s) > 1708/(N_s + 1)$ where Ns is a heat source parameter and $\widetilde{RA}$ is a critical Rayleigh number. This last problem is also solved numerically and the result compared with linear theory. The critical Rayleigh numbers given by energy theory are slightly less than those given by linear theory, this difference increasing from zero with the magnitude of the heat-source intensity. To previous results proving the non-existence of subcritical instabilities in the absence of heat sources is appended this result giving a narrow band of Rayleigh numbers as possibilities for subcritical instabilities.

In this paper we consider the effect of internal heat generation and a spatial variation of the gravity field on the onset of thermal convection in spherical shells. If the temperature gradient and gravity fields have the same spatial variation, then initially quiet fluids are subcritically stable. For these flows the effect of inertially non-linear disturbances is not destabilizing if the Rayleigh number is below the critical value set by linear theory plus ‘exchange of stabilities’. For subcritically-stable flows a principle of exchange of stabilities is not necessary; a stronger statement of stability for the same stability limit can be made. For the many cases calculated here in which subcritical instabilities can exist, the difference between the linear and energy limits is small and can be contracted only toward the energy limit by an improved linear theory.

The motion of turbulent jets of heavy salt solution injected upwards into a tank of fresh water has been compared with that of plumes which are initially buoyant but become heavy as they mix with the environment. The reversal of buoyancy in the latter case is produced by using fluids having a non-linear density change on mixing, a laboratory analogue of the density changes occurring at the top of a cumulus cloud due to evaporation. The behaviour in the two cases is quite different; salt jets reach a steady height about which only small fluctuations occur, while the plumes with reversing buoyancy exhibit violent regular oscillations. This phenomenon, which is clearly a property of the ‘evaporation’ and not just of the geometry, is suggested as a likely explanation of the observed oscillation of the tops of cumulus towers. Dimensional arguments have been used to relate the experimental results to the volume, momentum and buoyancy fluxes at the source. An application of one of the deduced relations to the atmosphere gives realistic periods for the cloud-top oscillations.

The approach to equilibrium in a non-equilibrium-dissociating boundary-layer flow along a catalytic or non-catalytic surface is treated from the standpoint of a singular perturbation problem, using the method of matched asymptotic expansions. Based on a linearized reaction rate model for a diatomic gas which facilitates closed-form analysis, a uniformly valid solution for the near equilibrium behaviour is obtained as the composite of appropriate outer and inner solutions. It is shown that, under near equilibrium conditions, the primary non-equilibrium effects are buried in a thin sublayer near the body surface that is described by the inner solution. Applications of the theory are made to the calculation of heat transfer and atom concentrations for blunt body stagnation point and high-speed flat-plate flows; the results are in qualitative agreement with the near equilibrium behaviour predicted by numerical solutions.

The effect of uniform rotation on surface-tension-driven convection in an evaporating fluid layer is considered both theoretically and experimentally. The theoretical analysis follows the usual small-disturbance approach of perturbation theory and leads, at the neutral state, to a functional relation between the Marangoni and Taylor numbers which is then computed numerically. In addition, it is shown analytically that, in the limit of rapid rotation, the velocity and temperature fluctuations are confined to a thin Ekman layer near the surface, and that Mc = 4·42T½ and ac = 0·5T¼, where Mc and ac are, respectively, the critical Marangoni number and the critical wave number for neutral stability, and T is the Taylor number.

The experimental part deals primarily with the flow pattern of a 50% solution of ethyl ether in n-heptane evaporating into still air. In this case, the convective flow is surface-tension-driven and its structure was observed using schlieren optics. In the absence of rotation, the flow shows a remarkable cellular pattern when the layer is shallow, but when the depth of the layer is increased the pattern quickly becomes highly irregular. In contrast, for T > 103, a cellular structure is always observed even for deep layers, a result which is attributable to the stabilizing effect of the Coriolis force. A further increase in T leaves the flow pattern unchanged except that the size of the cells is found to decrease as T−¼ which is in agreement with the results of the linear stability analysis.

Experimental evaluation of the radial momentum equation near the surface for an axisymmetrie turbulent wall jet is reported. The equation for flow contains six terms of magnitudes which cannot be neglected. The pressure gradient across the flow as well as along the flow is found to be of major importance. Thus, for a wall jet flow it is impossible to treat the radial and vertical momentum equations as independent of one another.

The flow field in the nose region of a blunt body in hypersonic flow is studied by considering the transport of vorticity and enthalpy. The entire region between body and shock is considered to be viscous, not necessarily thin in comparison with the nose radius of the body and to be of slowly varying density. The (given) post-shock vorticity need not be small and the density ratio ρ∞/ρs may either be small or near unity, the analysis being valid asymptotically at both limits.

It is found that the vorticity equation may be uncoupled from the total enthalpy equation if μ√ρ is constant. While the equations are not expected to be necessarily restricted to the immediate vicinity of the stagnation line, only there can the solution be written down explicitly; elsewhere, numerical integration is required.