The motion due to an oscillatory point source in a rotating stratified fluid has been studied by Sarma & Naidu (1972) by using threefold Fourier transforms. The solution obtained by them in the hyperbolic case is wrong since they did not make use of any radiation condition, which is always necessary to get the correct solution. Whenever the motion is created by a source, the condition of radiation is that the sources must remain sources, not sinks of energy and no energy may be radiated from infinity into the prescribed singularities of the field. The purpose of the present note is to explain how Lighthill's (1960) radiation condition can be applied in the hyperbolic case to pick the correct solution. Further, the solution thus obtained is reiterated by an alternative procedure using Sommerfeld's (1964) radiation condition.

An experimental investigation was undertaken of the flow produced by the inviscid expansion of air through a hypersonic nozzle. Stagnation enthalpy levels up to 4 × 107 J/kg were used, with initial dissociation levels approaching 90%. By measuring the flow velocity and the frozen dissociation fractions of oxygen and nitrogen, it was found that existing theoretical models served adequately to define the nozzle flow, at least for the purpose of conducting experiments involving reacting inviscid hypersonic flows about blunt bodies.

In this paper the first thirty-two axisymmetric modes for steady-periodic waves in viscous compressible liquids contained in rigid, impermeable, circular tubes are calculated. These results end long speculation over the effects of viscosity on guided acoustic waves. Sixteen of the modes belong to a family of rotation-dominated modes whose existence was previously unknown. The thirty-two modes were computed for a wide range of frequencies, viscosities and wave-lengths.

The modes were found through the use of the method of eigenvalleys, which also led to the discovery of backward-propagating waves, an exact analytical expression for the zeroth rotational mode eigenvalue, definitive boundaries between low and intermediate frequencies and between intermediate and high frequencies, and a new type of boundary layer, called a dilatational boundary layer.

The effects of a wavy permeable boundary on turbulent flow are investigated theoretically and experimentally, mainly in terms of the pressure distribution along the wavy boundary and the friction factors. A simplified theoretical analysis based on potential flow theory and a linear Darcy equation shows that the perturbations of the flow field have a phase shift relative to the wavy surface and that, owing to this phase shift, there results a net form resistance on the wavy surface. Experiments were conducted in two pipelines with different sizes of granular material lining the inside of the pipe walls. The diameter of the porous conduits varied sinusoidally. The experimental results show that there is a phase shift between the boundary wave form and the pressure distribution and that friction factors increase with Reynolds number even though the flow is within the normal fully rough regime.

A wide range of behaviour for turbulent forced plumes generated by vertical emission of heated or other buoyant fluid from finite sources in extensive and otherwise still uniform environments can be represented on a single non-dimensional diagram of characteristic heights, plotted against a parameter Γ, which for forced plumes represents the balance of flow conditions imposed at the physical source. The set of curves presented includes the maximum height of ascent for negatively buoyant plumes, and the height of transition from jet-like to plume-like behaviour above sources emitting buoyant fluid with excess momentum. The levels of various point and planar virtual sources are displayed also for comparison with earlier solutions. This scale diagram relates ascent and transition heights to the initial conditions at actual sources, in contrast to earlier presentations which have unduly emphasized virtual sources.

A scale diagram for maximum ascent heights in stably stratified environments permits choice of the range of source conditions for a specified height of ascent and ambient stratification.

To solve a mathematical problem involving a small parameter, it is customary to expand the solution in powers of that parameter. In singular cases the resultant linearized problem may be insoluble, and in some such cases it is appropriate to expand the solution in powers of the square-root of the small parameter. These cases are associated with bifurcation of the solution. The method is illustrated by applying it to the Falkner-Skan equation and to a problem in hydrodynamic instability. In particular, Hartree's conjecture, that near separation the skin friction vanes like the square-root of the appropriate parameter of the Falkner-Skan equation, is substantiated.

The magnetohydrodynamic and Boussinesq approximations are used on a fully ionized ideal fluid with a longitudinal magnetic field. The flow is in a direction normal to the gravity vector and all variations in velocity, density and magnetic field. The stability characteristics, mainly for normal-mode perturbations, are investigated. Two simple problems with discontinuous profiles are solved analytically. For a double shear layer, an appropriate range of magnetic field values destabilizes the flow. A long wave theory is presented and applied to several problems, some of which are destabilized by an appropriate magnetic field. Finally, the solution for continuous profiles is presented and shown to decay algebraically in time for any stable stratification.

The 33rd EUROMECH Colloquium on three-dimensional turbulent boundary layers was held in Berlin during 25–27 September 1972. Forty-two participants from six countries were present, and Professor R. Wille and the author organized the Colloquium. The papers presented could be clearly divided into two groups, one dealing with prediction methods and the other describing experimental results. References quoted give the titles of the papers presented at the meeting and refer to further work discussed at the Colloquium; there will be no other publication of the proceedings.

Vibrational relaxation of oxygen and nitrogen is shown to be important in determining the structure of weak shock waves in air. Of particular interest are waves with pressure jumps of 100Pa1 Pa ≡ 1 pascal = 1 N m−2. or less which are present in the atmosphere as sonic bangs. It is found that the structure of the waves depends on shock strength, ambient pressure, temperature and humidity.

The interaction of a gas cloud of specified mass, momentum and energy with an atmosphere in uniform motion is studied using the kinetic theory of gases. The Krook collision model is used to obtain analytically interpretable and numerically tractable results describing the spatial and temporal evolution of the cloud. The cloud originates from a continuum source and expands to a free molecular flow. It then begins to collide with the atmosphere, and is gradually transformed into a continuum flow diffusing through the atmosphere while being convected by the uniform motion.

An implicit predictor–corrector difference scheme is employed to study the propagation of spherical and cylindrical N-waves governed by the modified Burgers equation \[ \frac{\partial u}{\partial t} + u\frac{\partial u}{\partial x}+\frac{\nu u}{2t}=\frac{\delta}{2}\frac{\partial^2u}{\partial x^2}, \] where ν = 0, 1 or 2 for plane, cylindrical and spherical symmetry respectively. The numerical scheme is first tested by computing the plane solution and comparing it with theexact analyticsolution obtained by Lighthill (1956) through the Hopf-Cole transformation.

Our numerical solutions for the non-planar N-waves show that variation of the ‘lobe’ Reynolds number, which may be used as a measure of the importance of viscous diffusion, can be accurately determined by the analysis which is strictly valid only for large Reynolds numbers. This is true even when shock wave is well diffused end the ‘lobe’ Reynolds number is as small as ½.