Amongst the more important laboratory experiments which have produced concentrated vortices in rotating tanks are the sink experiments of Long and the bubble convection experiments of Turner & Lilly. This paper describes a numerical experiment which draws from the laboratory experiments those features which are believed to be most relevant to atmospheric vortices such as tornadoes and waterspouts.

In the numerical model the mechanism driving the vortices is represented by an externally specified vertical body force field defined in a narrow neighbourhood of the axis of rotation. The body force field is applied to a tank of fluid initially in a state of rigid rotation and the subsequent flow development is obtained by solving the Navier–Stokes equations as an initial-value problem.

Earlier investigations have revealed that concentrated vortices will form only for a restricted range of flow parameters, and for the numerical experiment this range was selected using an order-of-magnitude analysis of the steady Navier–Stokes equations for sink vortices performed by Morton. With values of the flow parameters obtained in this way, concentrated vortices with angular velocities up to 30 times that of the tank are generated, whereas only much weaker vortices are formed at other parametric states. The numerical solutions are also used to investigate the comparative effect of a free upper surface and a no-slip lid.

The concentrated vortices produced in the numerical experiment grow downwards from near the top of the tank until they reach the bottom plate whereupon they strengthen rapidly before reaching a quasi-steady state. In the quasi-steady state the flow in the tank typically consists of the vortex at the axis of rotation, strong inflow and outflow boundary layers at the bottom and top plates respectively, and a region of slowly-rotating descending flow over the remainder of the tank. The flow is cyclonic (i.e. in the same sense as the tank) in the vortex core and over most of the bottom half of the tank and is anticyclonic over the upper half of the tank away from the axis of rotation.

A solution to the hypersonic small disturbance equations is obtained for a class of two-dimensional bodies supporting logarithmic shock waves by reducing the partial differential equation to an ordinary differential equation. The body shape is calculated and shown not to be logarithmic if γ ≠ 1, where γ is the ratio of the specific heats of the gas.

In this paper we look at the problem of an undular bore entering still water. The effect of the boundary-layer at the channel bottom is considered. The motion is assumed to be laminar and inviscid, apart from the thin boundary layer, where the normal boundary-layer approximations are used to find the velocity components. The effect on the main flow then appears in the equations of motion as a shear stress.

Particle velocity autocorrelations of single spherical beads (46·5 μhollow glass, 87 μ glass, 87 μ corn pollen, and 46·5 μ copper) were measured in a grid-generated turbulence. The hollow glass beads were small and light enough to behave like fluid points; the other types had significant inertia and ‘crossing trajectories’ effects. The autocorrelations decreased much faster for heavier particles, in contradiction to previous experimental results. The integral scale for the copper beads was 1/3 of that for the hollow glass beads. The particle velocity correlations and the Eulerian spatial correlation were coincident within experimental error when the separation was non-dimensionalized by the respective integral scale. The data generated by the hollow glass beads can be used to estimate Lagrangian fluid properities. The Lagrangian time integral scale is approximated by L/u′, where L is the Eulerian integral scale and u′ is the turbulence intensity.

Measurements in the wake behind turbulent jets exhausting from a solid surface into a cross-wind indicate that vortex shedding occurs as in the case of flow past solid bluff bodies. The Strouhal numbers for flow past a circular and a blunt jet are in qualitative agreement with those for corresponding solid bodies, provided that the width of the spreading jet some distance from the surface is used rather than the jet exit plane dimension.

The initial-value problem for waves generated by ground motion near a shore is solved using linear shallow water theory and an exponential bottom profile. It is found that long waves can be trapped along the coast and travel with the deep water wave speed, (gh)½. The energy in these waves decays with x−½ instead of x−1 so that more energy would be observed on this coast than expected on the basis of deep water wave amplitudes.

Simultaneous measurements of wave elevation and atmospheric pressure on wind-driven sea waves were made using a vertical wave-sensing rod and a small (23 cm diameter) pancake-shaped styrofoam buoy in which was embedded a sensitive pressure transducer; the wave probe constrained the buoy to move with the waves only in the vertical direction. Care was taken to avoid contamination of the pressure signal with dynamic pressures caused by flow distortion around the buoy.

Results are presented as power and cross-spectra of wave elevation and pressure, spectra of the fluxes of energy and momentum from the wind to the waves, and spectra of ζ the fractional increase in wave energy per radian.

The phase shifts of the pressure signal are compared with the laboratory and field results of other investigators, and with the theoretical predictions of Miles's (1957) inviscid laminar model of wave growth. Agreement is reasonably good among the experimental results, but observed phase shifts are an order of magnitude larger than the theoretically predicted values.

Integrals under the momentum flux spectra are compared in all runs with the predictions of the standard empirical formula, and in two cases are compared with the values of the total wind stress as measured with a sonic anemometer; the indication is that a large fraction of the total flux of momentum from the air to the sea goes initially into the wave field.

The ζ spectra are compared with the field results of Snyder & Cox (1966) and with the theoretical predictions of Miles's (1957) model; agreement is again good between the field results while the theory underpredicts ζ by factors of between 5 and 8.

A simple dimensionless relation is found between ζ and the ratio of wind speed to wave phase speed.

The present paper, part 2, consists of an experimental investigation of the influence of a transverse magnetic field on the heat transfer of a conducting fluid (mercury) flowing in an electrically insulated pipe subjected to a uniform heat flux at the wall. Mean temperature profiles and heat transfer data are presented which demonstrate that the magnetic field inhibits the convective mechanism of heat transfer through its damping of the turbulent velocity fluctuations.

The stability of liquid layers in a porous medium under the action of viscous and surface forces is described. An extension of previous studies on the stability of a single interface in a porous medium is presented as the basis for solutions to many problems of practical interest where flow in porous media are involved.

The flow of a continuously stratified fluid into a contraction is examined, under the assumptions that the dynamic pressure and the density gradient are constant upstream (Long's model). It is shown that a solution to the equations exists if and only if the strength of the contraction does not exceed a certain critical value which depends on the internal Froude number. For the flow of a stratified fluid over a finite barrier in a channel, it is further shown that, if the barrier height exceeds this same critical value, lee-wave amplitudes increase without bound as the length of the barrier increases. The breakdown of the model, as implied by these arbitrarily large amplitudes, is discussed. The criterion is compared with available experimental results for both geometries.

In the theory of steady stratified rotating fluid motions developed by Barcilon & Pedlosky (1967) (hereafter referred to as B & P) for flows within a circular, cylindrical container it was asserted that the innermost boundary layer on the vertical side wall was absent to lowest order when the side wall is thermally insulated. That is to say, the buoyancy layer is not required to close the vertical mass flux. This result has been disputed in a recent note by Harrington & Johnson (1969) (hereafter referred to as H & J). It is the purpose of this note to reiterate the earlier result of B & P and to show that H & J is in error. Further the result is placed on firmer ground by using the fundamental dynamical characteristics of the inviscid interior and viscous boundary layers and by avoiding the algebraic snares of manipulating Fourier series.

High-speed digital computing methods are applied to the study of the statistical behaviour of turbulent velocity derivatives in a nearly isotropic turbulent field downstream of a grid. Higher-order correlations of turbulent velocity gradients, up to the eighth order, are measured. Contrary to the case of velocities, the higher even-order correlations of velocity gradients more clearly evidence the departure from a two-dimensional Gaussian probability distribution. Using non-Gaussian probability distribution laws the relations between different odd-and even-order correlations are obtained and compared with the experimental measurements. The conditions of similarity and isotropy are evaluated for the small-scale structure as evidenced by the behaviour of the turbulent velocity gradients. The concept of intermittency of the small-scale structure is also discussed.