A scattering configuration consists of a primary acoustic source S and a scattering body B, and we examine the effect of convection of S and B, at a uniform subsonic Mach number M, on the scattered field, for various types of source and scatterer. It is shown that if B is a compact rigid body scattering the near field of the source S it is not equivalent to a convected point dipole, but rather its pressure field is augmented by the quadrupole convection factor (1 − M cosθ)−3. If, on the other hand, the compact body B scatters the distant field of S, convective effects introduce an O(M) monopole field which does not vanish in the sideline directions. A number of problems are examined in which B is a rigid half-plane, and there it is shown that the effect of convection is to augment the pressure by $(1 - M \cos \theta)^{-\frac{3}{2}}$ in the case of diffraction of the field of a distant source S, and by $(1 - M \cos \theta)^{-\frac{5}{2}}$ for scattering of the near field of S. Effects associated with the multipole order of S are discussed, as are those arising from the satisfaction of a Kutta condition at the trailing edge of the half-plane, and the application of these results to current problems in aerodynamic sound is mentioned.

A numerical method incorporating some of the ideas underlying the wake source model of Parkinson & Jandali (1970) is presented for calculating the incompressible potential flow external to a bluff body and its wake. The effect of the wake is modelled by placing sources on the rear of the wetted surface of the body. Unlike Parkinson & Jandali's method, however, the body shapes that can be treated are not limited by the restrictions imposed by the use of conformal transformation. In the present method the wetted surface of the body is represented by a distribution of discrete vortices. Good agreement has been found between the pressure distributions predicted by the numerical method and the analytic expressions of Parkinson & Jandali for a ‘two-dimensional’ circular cylinder and flat plate. A flat plate at incidence and other asymmetric two-dimensional flows have also been treated. The method has been extended to axisymmetric bluff bodies and the results show good agreement with measured pressure distributions on a circular disk and a sphere.

The inviscid instability of heterogeneous swirling flows with radius-dependent density is investigated and secular relations for the instability growth rates for several different flow configurations are obtained from explicit solutions of the governing equations. It is found, in agreement with a sufficiency condition for the stability of such flows obtained earlier, that they are stable to both axisymmetric and non-axisymmetric infinitesimal modes whenever the density is a monotonic increasing function of radius and at the same time the radial variations in both the angular and axial velocity components remain small. The instability mechanisms present in these flows are both of centrifugal and of shear origin, the classical Rayleigh–Synge criterion being a condition for centrifugal stability. It is shown, via several counter examples, that the Rayleigh–Synge criterion for the stability of swirling flows is generally neither a necessary nor a sufficient condition when non-axisymmetric disturbances are considered or large shears exist in the flow. Very stable flows occur when the angular and axial velocity components have no radial variation and simultaneously the density increases with radius as is the case in a typical centrifuge.

A numerical solution of the complete Navier–Stokes equations of motion by means of an implicit finite-difference method is presented for the following developing-flow problem: a piston forced with constant speed through an infinitely long tube of circular cross-section. The transition of the velocity profile of an incompressible isothermal Newtonian fluid from the plug-flow profile in front of the piston to the parabolic profile of developed flow is analysed. Streamlines, vorticity distributions, velocity profiles, the excess pressure drop and the entrance length are given for Reynolds numbers from 0 to 800.

Experimental investigations of natural convection in a porous layer placed between two horizontal and isothermal plane surfaces have revealed a new type of convection as the Rayleigh number Ra* increases: fluctuating convection. A numerical study carried out on a two-dimensional model in order to simulate this phenomenon shows that, apart from the influence of the Rayleigh number, the aspect ratio A (length/height) of a vortical cell is the most important parameter for the occurrence of this type of convection. These quasi-periodic fluctuations induce important variations in the temperature field and in the streamlines. The total heat transport, as defined by the Nusselt number Nu*, varies within limits which may be separated by 80% of the mean value. Using the Galerkin method it is possible to deduce the conditions for the onset of convection from a state of pure conduction and also to define the critical conditions for the development of fluctuating convection from another perturbed state. A physical interpretation of the results is given for each type of convection. The results seem to agree with the experimental and numerical results obtained by different authors.

In this paper slender-body theory is applied to flexible bodies. The bodies are assumed to have a constant forward velocity normal to the crests of a regular train of two-dimensional waves and to move at a nearly constant depth. A flexible recoil mode is defined which is the dynamic counterpart of the stretched straight fish position defined by Lighthill (1960) for uniform flow conditions. Expressions are derived for the mean thrust and for the mean rate of working, and permit the evaluation of conditions for efficient propulsion. By properly adapting the motions of the body to the oncoming waves, energy can be extracted from the waves in such a way that it can be used for propulsion. This phenomenon may help to explain the high speeds that cetacea are observed to sustain over long periods of time.

Kraichnan's (1967) predictions concerning a simultaneous direct enstrophy cascade and inverse energy cascade for high Reynolds number two-dimensional turbulence are tested numerically using a variant of the eddy-damped quasi-normal approximation. For the initial-value problem, an analytic study using this theory shows that, in the zero-viscosity limit, energy and enstrophy are conserved for arbitrarily long times, contrary to the three-dimensional case, where the energy is conserved for only a finite time, after which it is dissipated. Non-local effects in the enstrophy inertial range, which are difficult to treat by conventional numerical schemes (Leith 1971; Leith & Kraichnan 1972), are shown to be representable by an additional diffusion term in the spectral equation. The resulting equation, including non-local effects, is integrated numerically. When enstrophy and energy are continuously injected at a fixed wavenumber, it is shown numerically that a quasi-steady regime is obtained where enstrophy cascades to large wavenumbers across a k−3 inertial range with zero energy transfer while energy flows indefinitely to small wavenumbers across a $k^{-\frac{5}{3}}$ inertial range with zero enstrophy transfer.

A baroclinic-type instability in a gas centrifuge heated from above is discussed. The instability is shown to be of overstable type, and estimates of the growth time scale and oscillation period of the unstable mode are given.

A discussion of the applicability of an effective-viscosity approach to turbulent flow suggests that there are flow situations where the approach is valid and yet present hypotheses fail. The general form of an effective-viscosity formulation is shown to be a finite tensor polynomial. For two-dimensional flows, the coefficients of this polynomial are evaluated from the modelled Reynolds-stress equations of Launder, Reece & Rodi (1975). The advantage of the proposed effective-viscosity formulation, equation (4.3), over isotropie-viscosity hypotheses is that the whole velocity-gradient tensor affects the predicted Reynolds stresses. Two notable consequences of this are that (i) the complete Reynolds-stress tensor is realistically modelled and (ii) the influence of streamline curvature on the Reynolds stresses is incorporated.

The phase velocities of axial disturbances to a free jet have been investigated experimentally. For a certain range of low Strouhal numbers previous theories predicted the existence of phase velocities exceeding the mean velocity of the jet. These ‘ultra-fast’ phase velocities were found in the present experiments too.

The forced oscillations due to a point forcing effect in an infinite or contained, inviscid, incompressible, rotating, stratified fluid are investigated taking into account the density variation in the inertia terms in the linearized equations of motion. The solutions are obtained in closed form using generalized Fourier transforms. Solutions are presented for a medium bounded by a finite cylinder when the oscillatory forcing effect is acting at a point on the axis of the cylinder. In both the unbounded and bounded case, there exist characteristic cones emanating from the point of application of the force on which either the pressure or its derivatives are discontinuous. The perfect resonance existing at certain frequencies in an unbounded or bounded homogeneous fluid is avoided in the case of a confined stratified fluid.

The steady, inviscid, axisymmetric, rotating flow past a prolate spheroid in an unbounded liquid is determined on the hypothesis that all streamlines originate in a uniform flow far upstream of the body. The similarity parameters for the flow are κ = 2Ωa/U and δ = a/b, where 2a and 2b are the minor and major axes and Ω and U are the angular and axial velocities of the basic flow. Solutions are obtained both by separation of variables in prolate spheroidal co-ordinates and through the slender-body limit δ ↓ 0 with κ = O(1). Forward separation is found to occur for κ > κ*, where κ* lies between 2·2 and 2·3 for 0 < δ [les ] 1. The velocity on the body, the upstream axial velocity and the wave drag are calculated for κ < κ*.

A model equation is derived which approximately describes the propagation of periodic surface waves in water of slowly varying depth. Numerical solutions to the model equation are obtained for the scattering of an incident plane wave by a conical island.

An approximation to the profile of given area with smallest drag in laminar flow is obtained (for Reynolds numbers between 103 and 105). It was shown previously by Pironneau (1974) that the skin friction on such a profile has to satisfy certain optimality conditions; the method used is based on these results. It was found that the optimum profile is long and thin (thickness-to-chord ratio about 10%), the front end being shaped like a wedge of angle 90° and the rear end like a cusp. The drag is very close to the drag on a flat plate of equal length.

Cavitation bubbles were produced by focusing giant pulses of a Q-switched ruby laser into distilled water. The dynamics of the bubbles in the neighbourhood of a solid boundary were studied by means of high-speed photography using a rotating-mirror camera with framing rates of up to 300000 frame/s. Bubble motion was evaluated from the frames with the aid of a digital computer using a graphical input device. Smoothed distance-time curves of different portions of the bubble wall were obtained also, allowing a reliable calculation of bubble-wall velocities (except at the actual instant of collapse). One of the numerical examples of the collapse of a spherical bubble near a plane solid boundary obtained by Plesset & Chapman could be realized experimentally. A comparison of the bubble shapes shows good agreement.