Turbulent energy spectra have been measured in a round air jet at high Reynolds numbers (Rλ = 710 to 780). The streamwise and cross-stream spectrum functions are well fitted by the (${\\frac{5}{3}$) power law predicted by the Kolmogoroff theory for an inertial subrange. The data are shown to be consistent with the local isotropy hypothesis and the constant in the Kolmogoroff spectrum function in the inertial subrange is evaluated. Effects of length and non-linear response of the hot-wire are considered.

The behaviour of cylinders of fluid injected vertically downwards into a similar stationary fluid has been observed with particular reference to the effect of a stable density stratification in the stationary fluid upon the penetration and upon the mixing between the injected and ambient fluids.

When the ambient fluid is of uniform density, it is found that the motion is approximately self-preserving, and that the energy decay rate per unit mass of moving fluid follows the same law as does the decay rate in a turbulent fluid.

The observations demonstrate that the effect of the density stratification in the ambient fluid is principally upon the gross motion and only slightly upon the smaller scales of motion.

Estimates are given of the maximum conversion of kinetic energy to potential energy, and of the ultimate loss of energy to buoyancy, as a function of a Richardson number determined from the initial conditions of volume, velocity, density gradient, density, and the acceleration of gravity.

This paper deals theoretically with some aspects of the influence of a non-homogeneous electric field on the laminar convective motion and heat transfer in paraelectric gas. i.e. a gas consisting of molecules having a permanent electric dipole moment. It is found that, due to the variation of the dielectric susceptibility with temperature, the electric field produces an electrical buoyancy force. Convective velocities and heat transfer in the gas near a heated surface are found to be increased or decreased according as the electrical buoyancy force acts with or in opposition to the net force of the existing pressure gradient and gravitational buoyancy force.

The equations of motion for a paraelectric gas in the presence of an electric field are derived in a simplified form by the use of approximations similar to those of Boussinesq (1903). An exact solution of these equations is presented for the problem of laminar convection flow, under a pressure gradient, between vertical concentric cylinders which are maintained at different electrostatic potentials and whose wall temperatures decrease uniformly with increasing height. Here the electric field induces a heated down-flow to be superimposed on the existing cooled up-flow (or heated down-flow).

Boundary-layer equations are also derived for the laminar convective motion due to a heated charged sphere. These equations are solved by an approximate method due to Squire (1938).

Measurements have been made of the perturbation magnetic field in front of a semi-infinite Rankine body, moving parallel to a uniform impressed magnetic field in a conducting fluid. The purpose of these experiments was to investigate the so-called upstream wake effect which has been predicted by theory. It is believed that these are the first experiments in which the upstream wake has been observed. Although the wake was found to exist as predicted when the Alfvén number is greater than one, its decay behaviour was remarkably different from that which was predicted. The solutions for an infinite medium predicted that in the wake the perturbations should decay inversely as the distance from the body. However, the experiments showed that the perturbations decayed exponentially. It was finally shown that this change in the decay behaviour was an effect of the walls and the conducting material surrounding the fluid.

The pressure field is found in closed analytic form for the region behind an arbitrary plane shock, which has encountered a thin aerofoil moving at supersonic speed. The solution may be used for wedges at small incidence to the air-flow around them, and for wedges yawed with respect to the shock plane through angles up to a limiting value which always exceeds 67·8°. The pressure distribution on the surface of a wedge is calculated in a number of examples illustrating separately the effects of shock strength, wedge speed, and angle of yaw.

An explicit determination is made of the velocity potential for the small-amplitude time-periodic excitation of a bottomless, heavy, incompressible fluid which results from an internal point source, assuming that the equilibrium free surface lies in a horizontal plane and taking account of the presence within the fluid of a thin rigid plane with a vertical straight edge. The surface-wave component of the potential is expressed by means of single quadratures for any relative disposition of the source and observation points and, apart from exponential factors involving the depths of the respective points, proves to have the same functional character as the steady-state velocity potential for the acoustic (or compressional) motion which is sustained by an infinite line source parallel to the straight edge of a thin rigid half-plane.

The problem of the turbulent boundary layer in two-dimensional, incompressible flow, which is continuously critical, i.e. on the point of separating, over part of its length is solved by combination of the Buri separation criterion with the boundary-layer momentum equation. In the latter an attempt is made to allow for transverse pressure variation and Reynolds stresses by over-estimating the contribution of skin friction. The Buri constant is taken to have a value of Γ =−0·04. Whereas Stratford and Townsend assumed that an initially noncritical boundary layer could be transformed instantaneously into a critical state by the application of an infinite pressure gradient at a point, in the present approach it is considered necessary to induce a critical state over a finite length, this state then being maintained downstream. These solutions are thus not comparable near the starting-point of the flow, but fair agreement is suggested at large distances downstream, with Stratford and Townsend's theoretical solutions and with Stratford's experimental data.

Comparison is also made with an ideal pressure distribution suggested by Stuart and the basis of optimization is discussed. It is suggested that the optimum flow might be similar in form to the continuously critical flow. The thesis that a continuously critical boundary-layer flow is ideal for large extents of the suction surface of an aerofoil is denied.

The paper concludes that the Buri criterion is valid but that in this case the Buri constant has a value of -0·04 rather than the accepted value of -0·06. Previous work by the author in connexion with cascade aerofoils is justified. The analysis predicts theoretical minimum diffusion lengths for given pressure rises provided that the initial boundary layer has achieved a critical condition.

The flow of liquid helium II at subcritical velocities can be described by hydrodynamic equations which assume the possibility of independent motions of the two fluid components, but difficulties arise in supercritical flows with forces of mutual friction between the component fluids. The extensive evidence that mutual friction is caused by scattering of the thermal excitations in the velocity fields of the quantized vortex lines suggests that the equations should include mutual forces which are large near the vortex-lines and negligible elsewhere. In their original theory, Hall & Vinen (1956) did assume this, and here the implications of the assumption are examined in detail. Serious difficulties are found in reconciling localization of the mutual friction with fully developed flow in channels, and it is suggested that, although the mutual friction arises from scattering near the vortex lines, the force on the superfluid is distributed uniformly over distances comparable with the distance between adjacent vortex lines.

From the conditions of energy and momentum conservation it is shown that all four interaction coefficients of the elementary quadruple interactions discussed in Part I of this paper are equal. A further conservative quantity is then found which can be interpreted as the number density of the gravity-wave ensemble representing the random sea surface. The well-known analogy between a random linear wave field and a mass particle ensemble is found to hold also in the case of weak non-linear interactions in the wave field. The interaction conditions for energy transfer between waves to correspond to the equations of energy and momentum conservation for a particle collision, the final equation for the rate of change of the wave spectrum corresponding to Boltzmann's equation for the rate of change of the number density of an ensemble of colliding mass particles. The stationary wave spectrum corresponding to the Maxwell distribution for a mass particle ensemble is found to be degenerate. The question of the irreversibility of the transfer process for gravity waves is discussed but not completely resolved.

The method of characteristics is used to calculate numerical solutions for the head-on collision of a shock wave with a centred rarefaction wave in the onedimensional unsteady flow of a perfect gas. It is found that, for sufficiently strong shock waves, the rate of increase in the strength of the shock as it propagates through the rarefaction is so great that the temperature behind the shock reaches extreme values.

An investigation is made into the possible types of similarity solutions that can describe the symmetric flow of a fluid into an empty spherical cavity. The flow is homentropic, and the fluid obeys a perfect gas law $p\; =\; k \rho ^{\gamma}$. Values of γ in the range 7 ≥ γ > 1 are discussed. In this range, we find that similarity solutions in which the flow accelerates into the cavity exist for $\gamma \textgreater {\frac{3}{2}$. For these solutions, the radius R of the cavity decreases as the nth power of time measured from the instant at which the cavity disappears. This power n increases monotonically as γ decreases, and attains the value 1 for $\gamma = {\frac{3}{2}$ Similarity solutions in which the cavity collapses with constant velocity are given by the value n = 1, and such solutions are possible for all values of γ in the range considered.

In an earlier paper Hall (1961) proposed a simplified model for the vortex core formed over a slender delta wing at incidence by the rolling-up of the shear layer that separates from a leading edge. This model enabled an outer inviscid solution and an inner viscous solution for the core to be obtained from the equations of motion. However the procedure used for the inner solution led to a number of defects: in particular, the matching of the inner and outer solutions seemed unsatisfactory. In the present paper the defects are avoided by using a different procedure. The first approximation, in the sense of boundary-layer theory, is sought. A solution, in special variables, is obtained which is in the form of an asymptotic expansion containing inverse powers of the logarithm of a Reynolds number. The leading terms of the expansion are computed, and the results confirm that the inner and outer solutions are properly matched.