In a two-layer liquid system non-linear resonant interactions between a pair of external (surface) waves can result in transfer of energy to an internal wave when appropriate resonance conditions are satisfied. This energy transfer is likely to be more powerful than similar transfers between external waves. The shallow water case is discussed in detail.

It is shown how a simple property of the spherical vortex model can be used to investigate the dynamics of a buoyant, expanding thermal. No details of the vortex motion are required, only the fact that the flow round the buoyant region is potential. The main result is a demonstration that there is a relation between the two constants C and α arising in the dimensional analysis (where in the usual notation w = C (Δr) ½) and r = αz), which have up till now been measured separately and treated as independent. The analysis has been extended to spheroidal thermals by calculating the virtual mass for the appropriate outline, and it has also been generalized to include thermals in which the total buoyancy is increasing with time.

Using these risults, and an earlier experimental verification that the mean angles of spread are nearly the same under various conditions of stability, it is suggested that the whole of the mean behaviour of a thermal can be calculated in two nearly independent steps. first, the density difference or Δ as a function of height may be calculated using purely kinematic equations of conservation. Secondly, the velocity is obtained from the local values of Δ and radius r, using a mean value of C, since this has now also been shown to vary little over a wide range of conditions.

The problem solved is that of the interaction between a laminar boundary layer on a semi-infinite flat plate and an oncoming shear flow of finite lateral dimensions bounded by uniform irrotational flow extending to infinity. The pressures along the plate and upstream of the same are deduced (to a linearized approximation) in the form of a Fourier integral based on the solution of a simpler periodic flow problem. It is found that while the assumption of an infinite, uniform shear flow gives asymptotically correct interaction pressure gradients on the plate near the leading edge, the pressure level even there (compared to upstream infinity) is strongly influenced by the boundedness of the external shear. At distances from the leading edge which are large compared to the lateral extent of the shear flow, the pressure gradients along the plate are shown to be vanishingly smaller than in the infinite shear case.

A critical review is given of theories dealing with viscous effects in shock tubes for cases in which the boundary layer is thin compared with the diameter. In particular an examination of the radial variation of flow quantities is used to show that the approach of Mirels (1957) is based on firmer ground than that of Trimpi & Cohen (1955). It is also shown that the small perturbation theories of these and other authors lead to an equation for running time identical in form to that derived by Roshko (1960) from an asymptotic analysis of boundarylayer leakage through the interface.

The flow of an incompressible elastico-viscous fluid between two parallel, infinite disks is investigated when one disk is held at rest and the other performs rotary oscillations about their common axis. It is found that the purely periodic primary motion has associated with it a secondary steady velocity distribution, as well as a secondary periodic motion with twice the frequency of the primary. The steady component of the secondary flow is discussed in detail.

A solution is obtained for steady, moderately sheared, three-dimensional flow past a wire grid of arbitrary resistance distribution which is placed normal to the axis of a duct of arbitrary but constant cross-section. The formulation presented is an extension of those given by Owen & Zienkiewicz (1957) and Elder (1959) for weakly shared, two-dimensional flow past wire grids. Unlike these earlier formulations, however, in the present study the equations of motion are solved without placing restrictions on the magnitude of variation of resistance across the grid. The resulting solution, taking account of streamline deflexions, is verified experimentally for moderately sheared flow past three grids constructed to produce three widely differing velocity distributions in a water tunnel of circular cross-section.

Solutions for two types of problems involving the energy equation for flows with velocities described by the Blasius solution are presented. The first type arises in flows with arbitrary initial distributions of stagnation enthalpy and with surfaces downstream of the initial station either with constant wall enthalpy or with zero heat transfer. Exact solutions in these cases are obtained for constant ρμ, and Prandtl number of unity; they are given in terms of complete orthogonal sets of functions which can be used to obtain first- and higher-order corrections for the effects of variable ρμ, non-unity Prandtl number, and deviations of the velocity field from that described by the Blasius solution.

The second type of problem pertains to flows with power-law descriptions of the wall enthalpy. Again the basic solutions are obtained for Prandtl number of unity and the effect of non-unity Prandtl number is treated as a perturbation.

Propagation of a transverse electromagnetic wave along a d.c. magnetic field and interaction with a moving shock wave is investigated. The direction of propagation is normal to the shock front. Solutions to electromagnetic fields, gas velocities and Doppler shifts in frequency are found in both the ionized and un-ionized gases. A frequency is obtained at which electromagnetic reflexion from the shock front is minimized. In the ionized gas behind the shock front a fast and a slow electromagnetic wave result. By adjusting the shock velocity the frequency of the slow wave can be either raised or lowered. This frequency change, however, is not the Doppler shift and, consequently, can be made much larger than the Doppler shifts encountered at non-relativistic velocities. The slow wave attenuates much less than the ordinary fast wave, and applications to diagnostics and communications through plasmas and laser-beam frequency multiplication may be possible.

A steady-state technique of heat-transfer measurement has been developed based on the method of Seban, Emery & Levy (1959) whereby energy is dissipated by the Joule effect in a thin metal sheet on the surface of a model. For the present application, use was made of very thin but mechanically resistant films of metal of very nearly constant thickness, obtained by a simple mirror-silvering technique. The present investigation was prompted by the desire to make very local measurements of heat transfer for application in regions where large variations in convective heat flux and therefore in temperature could be expected.

Comparison between theory and experiment has been made in the simple case of a flat plate with constant heat flux for which a rigorous computation could be made based on the theory of Chapman & Rubesin (1949). The model was so conceived that the heat losses were small enough to be neglected. Therefore no corrections, which are often inaccurate, were needed for the experimental results, contrary to what is generally done when using other techniques for heat-transfer measurements. The excellent agreement between theory and experiment gives complete confidence in the method. The theoretical analysis showed that the measurements are simply related to the results that could be obtained in the case of an isothermal surface, because of the constant ratio that exists between the corresponding heat-transfer coefficients.

In this paper the equations for Alfvén waves are examined and conditions necessary for the occurrence of resonance are determined. An experiment using liquid sodium inside a torus is described. Waves were generated by means of alternating current supplied to a coil around the torus. A strong resonance was observed at the fundamental frequency, and a weak resonance at three times this frequency. At the fundamental resonance the alternating magnetic field attained magnitudes more than 9 times the magnitude of the field that would have been generated in free space by the exciting current. The results were in good agreement with prediction.

A remarkably stable type of revolving hollow water jet was generated in a vertical pipe, fixed in the base of a large tank, by first establishing Borda free flow, in which the jet springs clear of the pipe wall. Swirl was then imparted to the oncoming water, and an air core formed in the jet which was of varicose shape with alternate swellings and contractions of both its inner and outer surfaces. The observed wavelengths are compared with the theory, in which inertia and surface tension but not viscosity and gravity are taken into account.

For flows in either rotating or stratified fluids, a technique is developed for solving initial-value problems using an Oseen approximation to the non-linear inertial terms in the equations of motion. The resulting equations for either application are similar. The solutions bear a strong qualitative resemblence to observed flows of both kinds, being characterized at small Rossby or Froude numbers by a blocked flow upstream of an obstacle and waves on the downstream side.

Experiments are described in which a spinning tube was initially filled with water and closed at both ends; when the water had acquired uniform angular velocity the tube was suddenly opened at one end and hence emptied by centrifugal action, so that a cavity progressed along it towards the far end. The velocity of the cavity was found to be steady and proportional to the speed of rotation over the range tested, which confirmed the supposition that gravity and viscosity had insignificant effects on the cavity motion. Contrary to expectation, since the cavity velocity seemed to be too large for it to occur, the ‘Taylor phenomenon’ was observed in the liquid ahead of the cavity; that is, the motion generated by the invasion of the cavity extended over a continually lengthening region beyond it.

The theoretical discussion in § 4 explains several features of the experiments satisfactorily, although the complete analytical problem has so far proved insoluble.

The stability of viscous flow between rotating cylinders with an axial flow has been investigated theoretically by Goldstein (1937), Chandrasekhar (1960, 1962), and Di Prima (1960); and experimentally by Cornish (1933), Fage (1938), Kaye & Elgar (1957), Donnelly & Fultz (1960) and Snyder (1962a). As was pointed out by Di Prima (1960) there were a number of discrepancies in the early work of the 1930's which were clarified in part by the papers of the 1960's. In turn, there appear to be certain small detailed differences in the more recent papers. In part it is these differences with which the present paper is concerned. In addition, the results of the previous theoretical investigations which are limited to the case in which the cylinders rotate in the same direction, are extended to the case of counter rotation.

The onset of steady, cellular convection driven by surface tension gradients on a thin layer of liquid is examined in an extension of Pearson's (1958) stability analysis. By accounting for the possibility of shape deformations of the free surface it is found that there is no critical Marangoni number for the onset of stationary instability and that the limiting case of ‘zero wave-number’ is always unstable. Surface viscosity of a Newtonian interface is found to inhibit stationary instability. A simple criterion is found for distinguishing visually the dominant force, buoyancy or surface tension, in cellular convection in liquid pools.

A thin, flexible hydrofoil has been used as a model to simulate the swimming of a two-dimensional fish in an ideal, incompressible fluid, as treated in recent theoretical papers. The apparatus is described in some detail and typical data are compared with the predictions of theory. An error analysis is given, showing that, within the expected errors and limits of validity of theory, experimental verification of theory is very good.

A dispersion relation is set up for transverse waves in a plasma with an ellipsoidal velocity distribution. It is shown that the most unstable wave has its wavenormal parallel to the shortest axis of the ellipsoid and its vector potential parallel or anti-parallel to the longest axis. The maximum possible amplification rate is then calculated. Ellipsoidal velocity distributions arise in any flow with an anisotropic pressure tensor. If the resulting instability leads to a microscopic redistribution of particle velocities, then the effective transport coefficients of the plasma are changed. In Particular it is shown that the effective viscosity is decreased, and becomes dependent on the local gradient of the macroscopic velocity.

Two sets of published data on an area 2700ft. by 1800ft. of sea surface in the North Atlantic are analysed by an optical computer which gives directly the directional spectrum. The results are compared with (i) those of other investigators obtained laboriously by using a digital computer, (ii) the frequency spectrum, and (iii) an empirical prediction.

Using identical equipment, an attempt was made to reproduce the unexpected flow reversals obtained by Sibulkin (1962) in his study of the vortex motion associated with draining a liquid from a vessel through an orifice in its bottom. Reversal of the initial direction of rotation was found only for counter-clockwise filling with large initial heads and settling times, unless during settling or draining of the vessel a shock was applied to the system, in which case the tendency to reversal was generally more pronounced with clockwise filling. Re-reversal of the motion was also observed in a number of cases. An alternative explanation is proposed, based on a consideration of the surface waves generated by a shock.

The boundary layers due to finite viscosity and magnetic diffusivity are studied in relation to two models of the flow of a conducting fluid past a body in an aligned magnetic field. In each case it is deduced that the growth of the boundary layer may have substantial effects, such as to raise doubts about the validity of the assumed basic flow patterns.