A laboratory model of a tornado vortex has been produced, incorporating two features which are believed to be important to the understanding of the atmospheric phenomenon, but which have been largely ignored in previous studies. First, it has been shown that a vortex can be driven from above by a mechanism analogous to convection in a cloud, and that density differences within the funnel itself are not essential. Associated with this mechanism of formation is a circulation in the vertical, with an upflow in the centre surrounded by a compensating annular downflow. Secondly, the bottom boundary is seen to have a strong influence on the vortex, since the down and up flows are linked there by a rapid radial inflow in a thin boundary layer.

In the present paper an approximate theoretical description of such a vortex is proposed. The interior and boundary layer flows are first examined separately, and then a condition is sought which makes the two solutions consistent. The starting-point of the theory is the assumption of a form of stream function which describes a circulation in the vertical having the essential features of that observed. The result of the matching procedure is to fix both the form of the tangential velocity profile, and the relative magnitudes of the three components of velocity. These deductions are not critically dependent on the assumed form of the motion in the vertical, and are in good agreement with the first measurements in the laboratory vortices, though the quantitative experimental results are not emphasized here.

The directional spectrum of wind-driven surface waves has been measured under conditions of limited fetch, in order to check the predictions of the Phillips–Miles theory of wave generation (Miles 1960). The expression obtained for the directional spectrum in this theory involves the spectrum of the atmospheric pressure fluctuations, but it is possible to obtain theoretical estimates of the major features of the directional spectrum without knowledge of the pressures. Specifically, it is possible to predict the frequency at which the power spectrum should peak, and, for the higher frequencies, the range of azimuth over which high spectral values should be observed; for the lower frequencies the theory indicates a bimodal distribution in azimuth (Phillips's resonance waves), and gives the angle of travel relative to the wind as a function of frequency.

The results of the measurements are in fairly good agreement with the theoretical predictions for the higher frequencies. The asymmetry of the fetch results in the prediction that the waves will travel at an angle to the wind which varies with frequency, and this was observed. The range of azimuth over which the spectral density is high is also close to the theoretical prediction. For the low frequencies the bimodal distribution was not observed: the waves were found to have a single predominant direction of travel at each frequency. However, this direction conformed closely to that of one of the two wave trains predicted by Phillips, and its variation with frequency was also that given by the theory. There is reason to suppose that the peculiarities of the experimental site may be responsible for the absence of the second wave train, especially as it would be difficult to account for the observed effects on any basis other than that of Phillips's theory.

The assumptions of the shock-expansion method are re-examined. Although the shock-expansion method and Whitham's rule are used to treat two different classes of problems, certain similarities between these two methods are noted. It is suggested that a single procedure leads to solutions for the entire flow field for both classes of problems.

An approximate expression is obtained for the force on an arbitrary body executing slow vibrations in a viscous fluid.

The equation which was proposed for the calculation of forces on a sphere accelerating in a viscous fluid is verified by comparing the velocities of spheres falling under gravity in a viscous fluid with those calculated from the equation.

Results of experimental investigations of vibrational relaxation regions of shock waves in nitrous oxide are reported in this paper. The Mach-number range covered was from 1·5 to 7·5 and the photographs of the shocks were made using a Mach-Zehnder interferometer and a spark source. The experimental and calculated values of the over-all density ratio were found to be in good agreement, and the values of the relaxation frequencies were consistent with the data of other workers.

The shape of a jet of Newtonian liquid issuing from a capillary needle into air is considered. The results of two theoretical approaches are presented. One approach is a perturbation analysis about the final state of the jet and the other is a boundary-layer analysis near the point of jet formation. Comparison of the predictions with experimental jet shapes shows them to be in semi-quantitative agreement. Especially interesting is the presence of a ‘discontinuity’ in the empirical exponential decay rate of the jet radius occurring at a Reynolds number somewhere between 14 and 20 and the correspondence of this discontinuity with the peculiar behaviour in this range of the Reynolds number of the theoretical eigenvalue.

The characteristic lengths of the oscillating wakes of bluff bodies is discussed; in particular, those used in the universal non-dimensional frequencies proposed by Roshko (1954b) and Goldburg, Washburn & Florsheim (1965). It is concluded that these are equivalent at high Reynolds number. A closer examination leads to the conclusion that there are two simultaneous characteristic lengths; the scale of the formation region, and the width to which the free shear layers diffuse. Discussion of the mechanics of the formation region results in a physical basis for the determination of the frequency by these two characteristic lengths. The ideas developed are applied to the effects of splitter plates in the wake. The possibility of a high-Reynolds-number symmetrical formation region is suggested as an explanation of the very small lift values observed in the absence of free-stream disturbances.

A procedure is introduced to extend the usefulness of some perturbation solutions previously presented by Libby & Fox (1963) and Fox & Libby (1964). The perturbations are now formulated about a Blasius solution with an unknown origin. This origin, an additional degree of freedom, is selected, in the spirit of local similarity, so that it will yield a better approximation to the initial profile. With this modification the basic solution will handle a much wider class of problems successfully. Numerical examples are presented to demonstrate the improved accuracy and applicability of this new scheme.

An experimental study has been made of the motion of long bubbles in closed tubes. The influence of viscosity and surface tension on the bubble velocity is clarified. A correlation of bubble velocities in vertical tubes is suggested and is shown to be useful for the whole range of parameters investigated. In addition, the effect of tube inclination angle on bubble velocity is presented, and certain features of the flow are described qualitatively.

Existing data on the condensation of steam and moist air in supersonic nozzles are compared with predictions based on nucleation and drop-growth theory. It is concluded that, if the surface tension is assumed independent of curvature, and the classical liquid-drop theory (based on a stationary liquid drop) is used, the theory is in general agreement with the data. The effects of uncertainties in cluster surface energy and also of the large corrections to nucleation theory due to the ‘gasification’ concept are examined. The gasification correction is in accord with experimental data only if the surface tension is considered to rise significantly with curvature. In neither case can the Tolman or Kirkwood–Buff equations be supported. A review of existing data shows that there is some question as to the appropriate value of the condensation coefficient but this is of little consequence as long as the accommodation coefficient for the liquid–vapour surface is taken to be unity. The usefulness of the nozzle experiments for testing the validity of nucleation theory is demonstrated.

The present paper studies the interaction between non-equilibrium ionization phenomena in a plasma and the non-uniform flow of that plasma. The characteristics of non-equilibrium conditions are reviewed for the uniform flow situation in which electric and magnetic fields may exist. In order to permit study of the non-uniform flow situation a single-fluid theory is proposed in which the electrical conductivity is assumed to be a function of the absolute magnitude of the current density. The resulting highly simplified system of equations are then used to formulate the Hartmann-flow problem. For this case the formerly linear problem becomes non-linear. Despite this, solutions to within a quadrature are obtained when the Hall effect is neglected. The more complex problem including the Hall effect is solved numerically. Solutions showing velocity and current profiles are given. For certain values of the parameters governing the problem it is shown that no solutions exist.