The mechanisms which initiate secondary flow in developing turbulent flow along a corner are examined on the basis of both energy and vorticity considerations. This is done by experimentally evaluating the terms of an energy balance and vorticity balance applied to the mean motion along a corner bisector. The results show that a transverse flow is initiated and directed towards the corner as a direct result of turbulent shear stress gradients normal to the bisector. The results further indicate that anisotropy of the turbulent normal stresses does not play a major role in the generation of secondary flow. Possible extensions of the present results to other related flow situations are ahstrated and discussed.

A recent investigation of hydromagnetic waves in a rotating fluid has revealed certain ‘valve’-like critical levels associated with each wave which can be effectively penetrated from one side only. This effect is illustrated in the present paper by means of two further examples, namely (a) the propagation of hydromagnetio-gravity waves in a non-uniform magnetic field, and (b) the propagation of internal gravity waves in a wind which, though unidirectional, is both horizontally and vertically sheared.

The nonlinear stability of a liquid film adjacent to a supersonic gas stream is investigated. The gas is assumed to exert a mean shear stress at the liquid/gas interface which in turn establishes a linear mean velocity profile in the liquid. The analysis takes into account the pressure perturbation exerted by the gas on the liquid assuming the disturbed gas motion to be inviscid and the mean gas velocity profile to be uniform. The problem is formulated within the long wave approximation, and solutions are obtained for finite amplitude waves by using the method of multiple scales. The results predict the existence of finite amplitude periodic waves, in qualitative agreement with recent experimental observations.

Steady, supersonic, dissipative, three-dimensional, axisymmetric flow is considered. A system of Burgers-type equations is shown to govern the flow field. In inviscid regions the Whitham theory gives the limiting form. Dissipative effects ultimately engulf the inviscid zone and at sufficiently large distances from the body the flow is governed by linear dissipative theory. The flow field is divided into zones based on the presence or absence of nonlinearity and dissipation. Estimates and criteria which describe the extent of these zones are given.

The low Mach number sound field induced by the motion of line vortex filaments coupled to a two-dimensional semi-infinite duct is determined by means of a singular perturbation technique. Using the method of matched asymptotic expansions, solutions for the sound field are obtained by matching with an ‘inner’ region of incompressible flow. The radiation field induced by the emergence of a single vortex from the channel exhibits the edge scattering effects typical of half-plane problems. The sound field intensity is found to have angular dependence on sin2½ θ, where θ = 0 defines the exterior axis of symmetry. When a vortex pair propagates out of the duct however, the special symmetry of the fluid motion causes cancellation of the scattered field from the duct edges. In that case the sound field is driven from sources located at the duct exit. We show that this result is consistent with the general theories of both Curle and Powell. The sound field is essentially induced by a dipole at the exit plane of the duct, part of which drives a coupled weak monopole, while the remainder corresponds to an axial ‘edge force’ originating in the r−½ velocity singularities at the duct edges.

A linear stability analysis is applied to a stratified, thermally radiating, un-bounded shear layer. Temperature disturbances are assumed to be optically thin. Both viscous and inviscid neutral stability boundaries are determined numerically for hyperbolic-tangent mean velocity and potential-temperature profiles. For these profiles, long-wavelength disturbances are completely destabilized (the critical Richardson number Ric → ∞ as the wavenumber k → 0) in the inviscid limit. A similar situation is found for the case of discontinuous step-function profiles. However, in contrast to the non-radiating problem, the functional form of the neutral stability boundary is not the same for both the continuous and discontinuous profiles in the limit k → 0. Application of the viscous results to the atmospheres of the earth and Venus yield critical Richardson numbers in excess of ¼.

A survey of the density field in the immediate vicinity of Jarvis Island was made in April 1971. The island is isolated and is situated in the Pacific Equatorial Undercurrent, thus presenting the opportunity to study a high Reynolds number (∼ 109) stratified shear flow. Large deflexions of the isopycnals were observed near the island. Solutions derived from the perfect-fluid equations of Drazin (1961) axe in reasonable agreement with the observed mass field in the upstream region. Downstream, a wake region was apparent, but the dynamics of the wake are obscure. A coefficient of pressure deficit in the wake is in the same range as values computed from homogeneous laboratory flows, but baroclinic effects are observed.

The present paper considers the behaviour of a two-dimensional inviscid bubble when placed in viscous fluid whose velocity at large distances varies parabolically, and whose motion is governed by the equations of Stokes flow. For arbitrary values of the surface tension a t the bubble interface, this free boundary problem can be reduced to a coupled pair of transcendental equations.

When surface tension effects are large, the cross-section of the bubble is nearly circular. In the symmetric situation, with the bubble at the centre of a parabolic velocity profile, a reduction of the surface tension first produces a fattening at the rear of the bubble which then distorts further to form a re-entrant cavity. The solution also shows that the bubble moves faster than the undisturbed fluid velocity at its centre. When in an asymmetric position, the bubble has a drift velocity taking it towards the symmetric position.

The asymptotic solution for large time of the initial-value problem for weakly nonlinear wave systems is obtained by the method of matched asymptotic expansions in the case in which the linearized problem is slightly unstable. The linearized solution is valid until its small exponential growth overcomes the algebraic decay due to the dispersion of the initial energy. For larger times the nonlineax terms become important, but there are no additional dispersive or diffusive effects. For the non-diffusive case an exact solution which enables the explicit verification of the asymptotic results is found.

The structure of a supersonic laminar boundary layer near a flat plate is examined when fluid is injected into it with velocity of O(ε3U*∞) over a distance of O(L). Here U*∞ is the undisturbed fluid velocity, L the length of the plate and ε−8 is a representative Reynolds number. An essential requirement of the theory is that separation must have occurred upstream of the blow through a free interaction. It is assumed that between separation and the blow the reversed flow region has a wedge-like shape, of semi-angle in which O(ε2), the fluid velocity has decayed to insignificant values at points just upstream of the blowing region. The blown fluid fills this wedge and the favourable pressure gradient necessary to drive this fluid downstream causes the boundary of the wedge to curve until at the end of the blow it is parallel to the plate. Explicit expressions for the pressure variation and boundary-layer thickness are worked out using a (crucially) modified form of the Cole-Aroesty theory. The relation. between the strong injection studied here and massive injection, when the blowing velocity is of O(U*∞), is also discussed.

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.

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.

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.

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.