A hot-film anemometer has been used to investigate the mean velocity and turbulence intensity distributions in turbulent radial jets. A geometric parameter termed the constraint ratio, defined as the ratio of nozzle diameter to separation distance, is shown to characterize radial-jet behaviour. Large values of the constraint ratio typify ‘constrained’ radial jets, for which the nozzle walls constrain the flow leaving the orifice to be parallel; a small constraint ratio is representative of two opposing free axisymmetric jets, the collision of which produces an ‘impinged’ radial jet. It is found that the well-behaved constrained radial jet spreads at the same rate as does the familiar plane jet, whereas the impinged radial jet spreads at a rate more than three times as fast. Neither type of radial jet is amenable to a self-similar analytic solution; however, while the impinged jet is shown to require numerical solution techniques, an empirical solution for the constrained jet is demonstrated.

The Lagrangian and Hamiltonian for nonlinear gravity waves in a cylindrical basin are constructed in terms of the generalized co-ordinates of the free-surface displacement, {qn(t)} ≡ q, thereby reducing the continuum-mechanics problem to one in classical mechanics. This requires a preliminary description, in terms of q, of the fluid motion beneath the free surface, which kinematical boundary-value problem is solved through a variational formulation and the truncation and inversion of an infinite matrix. The results are applied to weakly coupled oscillations, using the time-averaged Lagrangian, and to resonantly coupled oscillations, using Poincaré's action—angle formulation. The general formulation provides for excitation through either horizontal or vertical translation of the basin and for dissipation. Detailed results are given for free and forced oscillations of two, resonantly coupled degrees of freedom.

The viscous damping of cnoidal waves progressing over a smooth horizontal bed is investigated. First approximations are derived for the attenuation of wave height with distance and for the friction coefficient at the bed. Attenuation coefficients are larger than those predicted on the basis of shallow-water sinusoidal wave theory and, unlike the case of sinusoidal waves, they are not independent of wave height. The limiting case of the solitary wave, considered previously by Keulegan (1948), is also discussed.

A boundary-layer model, based on computational results, describes a number of features of two-dimensional convection in a porous medium: the heat flux, velocity, length and temperature scales and the pattern of flow. The cell structure is different from that for convection in a viscous fluid. The model is valid for a limited range of the Rayleigh number.

When evaporation takes place in a surrounding vacuum, the expanding flow from a cylindrical surface is expected to start subsonic and to become supersonic in a short distance. A detailed treatment of this transition is given based on moment equations derived from the BGK model equation using an ellipsoidal approximant to the distribution function. Asymptotic solutions are developed for large source Reynolds numbers and compared with previous treatments. For moderate source Reynolds numbers a numerical procedure is used. In the latter case the treatment predicts that the flow never approaches a state of translational equilibrium.

The hydrodynamic stability of a pure liquid undergoing steady rapid evaporation at reduced pressure is examined using linear stability analysis. Results show that the rapidly evaporating liquid is unstable to local variations in evaporation rate, local surface depressions being produced by the force exerted on the surface by the rapidly departing vapour and sustained liquid flows being driven by the resultant shear exerted on the liquid surface by the vapour. The coupling of this ‘differential vapour recoil’ mechanism to the Marangoni effect is investigated and the importance of inertial heat transfer, fluid inertia and viscous dissipation at the interface to system stability is resolved.

We discuss non-axisymmetric instability of a thin cylindrical sheet of a gas which rotates concentrically with a rigidly rotating environment. For the sake of simplicity, we restrict ourselves to a linear single-mode analysis of a two-dimensional disturbance for which the axial component of the wavenumber vector vanishes. We further restrict ourselves to two limiting cases. In case 1 the gas can be treated as incompressible, while in case 2 the effect of radial stratification caused by the centrifugal force is extremely strong. In case 1 there are two unstable modes: a travelling and a stationary disturbance with respect to a system of co-ordinates which rotates with the environment. For each disturbance, we show the domains of instability on ρ vs. ω diagrams, where ρ is the density and ω is the angular velocity of the sheet non-dimensionalized with respect to those of the environment. A negative-viscosity phenomenon is also described. In case 2 both the travelling and the stationary disturbances are stabilized by the strong radial stratification. An outline of a WKB method of approximation is given.

A numerical investigation of vortex breakdown has been undertaken in an attempt to understand its properties, and the mechanisms responsible for it. Solutions of the full steady axisymmetric Navier—Stokes equations for breakdown in an unconfined viscous vortex have been obtained for core Reynolds numbers up to 200, for a two-parameter family of assumed upstream velocity distributions. Diffusion and convection of vorticity away from the vortex core, and the strong coupling between the circumferential and axial velocity fields in highly-swirling flows, are shown to lead to stagnation and reversal of the axial flow near the axis. The various theories of vortex breakdown are considered in light of the present numerical solutions.

A more rigorous proof is given of the validity of a generalized Prandtl—Glauert technique for caculating the solution to time-dependent small perturbation flows. The method, first used by Miles (1950a) for the airfoil problem and later applied by Amiet & Sears (1970) to more general problems, allows calculation of the term of first order in frequency. Anomalous behaviour for the two-dimensional problem is examined in detail and found to be limited to those two-dimensional cases which include shed vorticity downstream of the body. This anomaly, which precludes using the method for these cases, results from the need to satisfy a velocity boundary condition on the body. For this purpose the velocity must be calculated from the basic variable, the pressure, through an integrated form of the momentum equation. It is in thus calculating the velocity that the anomaly occurs. The method can be applied to both the two-dimensional case without shed vorticity and the general three-dimensional case.

This paper describes a prototype model experiment designed to test the principle that the ‘excess’ noise of a jet issuing from a conical nozzle can be significantly diminished by reducing the maximum pressure gradient in the flow. The experiment uses a water jet containing flow inhomogeneities in the form of air or helium bubbles exhausting through a conventional conical nozzle or a specially contoured ‘bellmouth’ nozzle. It is argued that the level of the internally generated noise is controlled by the mean-flow pressure gradient, and substantial reductions in the sound level are recorded with the bellmouth nozzle. Certain features of the acoustic pressure signatures of the two-phase flow are examined in detail, in particular a rather surprising absolute difference in the sound pressure levels produced when helium rather than air bubbles are used under otherwise identical mean-flow conditions. Theoretical arguments are advanced which appear to explain the principal features of the observations.

Methods of linear hydrodynamic stability are applied to analyse the stability of the isothermal Newtonian tubular film flow model of the industrial film-blowing process. The infinitesimal disturbances are assumed to possess axisymmetry. The relevant eigenvalue problem is formulated. A straightforward numerical scheme is developed to deal with the problem. Results are presented in the form of neutral-stability curves in the relevant parameter space. The significance and relevance of these to the industrial process are briefly discussed.

The discrete-cilia approach, or cilia sublayer model, is considered for propulsion of ciliated micro-organisms. Natural periodicity assumptions enable us to obtain a readily usable expression for the velocity where dependences on the direction of propulsion of the metachronal wave and on the time are not averaged out. Thus instantaneous interaction of the cilia with the fluid is calculable, and time-dependent velocity profiles are obtained. Calculations show that the velocity above the cilia sublayer is time independent and uniform. Closer to the bases fluid velocity fluctuations are large.