The most notable feature of the magnetohydrodynamic flow at large distances from a three-dimensional body is the formation of two wakes, within which vorticity and electric current are confined. In this paper results are obtained for the effective diffusivity and the relation between current and vorticity in each wake, for the balance between the strengths of the disturbances in the wakes and in the irrotational current-free flow outside, and for the lift and drag forces acting on the body. The final answers take the form of remarkably simple extensions of the corresponding formulae for non-conducting flow. In spite of the extra wake and the presence of a magnetic as well as a velocity field, the flow perturbation at large distances still has only three degrees of freedom.

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.

It is argued that the heat transfer between a roughened surface and a stream of incompressible fluid flowing over it is dependent on both the viscosity and thermal conductivity of the fluid even when the roughness is large enough for viscosity to have ceased to affect the skin friction.

Concentrating on closely spaced roughness, sufficiently large for the skin friction to be independent of Reynolds number, a simple model is constructed of the flow near the surface. It consists of horseshoe eddies which wrap themselves round the individual excrescences and trail unsteadily downstream; the eddies are imagined to scour the surface and thereby to transport heat between the surface and the more vigorous flow in the neighbourhood of the roughness crests. Taken in conjunction with Reynolds analogy between temperature and velocity distributions in the fluid away from the surface, the model leads to an expression for the rate of heat transfer which contains a function of the roughness Reynolds number and the Prandtl number of the fluid whose detailed form is found by appeal to the limited experimental data available. An order-of-magnitude argument suggests that the functional form established empirically is consistent with the assumed model of the flow close to the surface.

The object of the work is to establish a basis for the analysis of experimental data and for their extrapolation with respect to Reynolds number and Prandtl number.

The flow of a jet directed normal to a uniform, steady cross-wind is considered. Experimental results show that for various jet strengths, the position of the jet in space, when stretched by the ratio of jet to cross-wind momenta, is described by a single function. Exceptions exist at very low velocity ratios where a shift of the potential core is evident. A natural system of axes is used to define important directions of the flow. The integrated equation of motion along the primary jet flow direction is made dimensionless after the general method of Morton (1961) and a virtual source is defined for the flow. It is shown that a single functional behaviour of the axial jet velocity exists for various velocity ratios if the jet is considered to originate from this source. Lateral velocity profiles show a similarity when scaled by appropriate lengths and velocities but true self-preservation is not attained.

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.

The previously established criterion for the stability of a vortex sheet with respect to two-dimensional disturbances in a compressible fluid is extended to three-dimensional disturbances, and it is shown that disturbances travelling at sufficiently oblique angles with respect to the undisturbed flow are unstable. Slip-line instability downstream of a Mach reflexion is discussed briefly.

This investigation is concerned with the phenomenon of a gas jet impinging on and penetrating into a liquid. The study has been restricted to the cases of circular and plane jets penetrating a liquid at right angles. Both ‘free streamline’ and turbulent jets were considered. The phenomenon was analysed from two viewpoints. The first, a stagnation-pressure analysis, related the depth of the surface depression or cavity to the stagnation pressure based on the centre-line velocity of the jet in the neighbourhood of the surface. The second, a displaced-liquid analysis, related the weight of the liquid displaced from the cavity to the momentum of the jet.

Numerous experiments were conducted in which the cavity depth, diameter or width, and peripheral lip height were measured. The role of surface tension in affecting the cavity depth was considered and the phenomenon of drop formation was examined. Some attention was given to the case of a plane jet impinging on a moving liquid. It was found that the experimental data fit into the framework of these analyses quite consistently.

The feasibility of an experiment to measure the recombination rate of oxygen is examined using the ideal-dissociating-gas model. The experiment is to be performed in a shock tube, the shock-heated (and dissociated) gas being cooled by passing it through a Prandtl-Meyer expansion, and then allowed to recombine in a constant-area channel. At appropriate densities and shock Mach numbers it is found that recombination takes place in a distance suitable for a laboratory experiment.

Using this technique, the recombination rate of oxygen has been measured at 2700 ˚K. To determine the recombination rate, the absorption of ultraviolet light at a wavelength of 2283 å measured 11 cm downstream of the expansion was compared with absorptions calculated for various values of the recombination rate constant.

The measured value of the recombination rate constant of oxygen is in agreement with values calculated from dissociation rate measurements.

Small spheres of the same size but of relative density varying from 0·92 to 1·25 were injected in turn into a horizontal water pipe, in which the flow was turbulent and the mean velocity was constant. A cross-section near the outlet was illuminated; the positions of the spheres as they crossed it were measured by photography, and the relation was established between the terminal velocity of the of the spheres in water and the vertical diffusivity. The velocity of the spheres along the pipe was found to be somewhat different in the galvanized steel and Perspex lengths of which the pipe was composed. The dispersion of the times of transit of the spheres increased slightly with their densisty. For purposes of comparison the theoretical velocity along the pipe was also calculated from the photographic measurements.

The Wiener-Hopf technique is applied to solve the linearized problem of a two-dimensional compound gas jet, i.e. a jet embedded in a gaseous stream of finite width. The solution is found for all combinations of supersonic and subsonic flows in jet and stream. The general nature of the solution when only one of the flows is supersonic varies according as the value of a certain quantity mk, depending upon the gas constants, Mach numbers and widths of streams, is greater than or less than unity. When mk= 1 the solution appears to be invalid and it is suggested that, in this critical case, a steady flow (regarded as the limit in time of an unsteady flow) may not exist. It is further shown that the solution propounded by Pai (1952) for a supersonic jet embedded in a subsonic stream is simply the asymptotic form of the general solution. The findings of Pack (1956) for a supersonic jet in a supersonic stream are confirmed and extended.

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 in the mixing region of a 1 in. diameter cold air jet are described for Mach numbers ranging from 0.2 to 0.55. The statistical characteristics of the turbulence in the first few diameters of the flow may be expressed in terms of simple kinematic similarity relationships. These are based on the jet diameter and the distance downstream from the jet orifice as length-scales, and the inverse of the local shear as a time-scale. The experiments show that the integral time scale of the turbulence in a frame convected with the maximum energy of the turbulent motion is inversely proportional to the local shear.

The most interesting result obtained is that the local intensity of the turbulence is equal to 0.2 times the shear velocity. This velocity is defined as the product of the local integral length-scale of the turbulence with the local shear. The local intensity is defined as the R.M.S. value of the local velocity fluctuations divided by the jet efflux velocity. It was found that the length-scale is proportional to the distance from the jet orifice, while the maximum shear is also related to this distance as well as to the jet efflux velocity. These two similarity relations break down close to the jet orifice and change beyond the first six or so diameters downstream. The convection velocity is not equal to the local mean velocity but varies slowly over the region of maximum shear when it is just over half the jet efflux velocity. The measurements of other observers fit the relationships obtained quite well. From these relationships it is possible to calculate the noise generated by the mixing region of a given jet directly, using expressions derived by Lilley (1958).

The concept suggested by Batchelor that motion of a marked particle in turbulent shear flow may be similar at stations downstream from the point of release is applied to a variety of diffusion data obtained in the laboratory and in the surface layer of the atmosphere. Two types of shear flow parallel to a plane solid boundary are considered. In the first case mean velocity is a linear function of log z (neutral boundary layer) and in the second case the mean velocity is slightly perturbed from the logarithmic relationship by temperature variation in the z-direction (diabatic boundary layer). Besides the parameters introduced in previous applications of the Lagrangian similarity hypothesis to turbulent diffusion, the ratio of source height to roughness length h/z0 is shown to be of major importance. Predictions of the variation of maximum ground-level concentration for continuous point and line sources and the variation of plume width for a continuous point source with distance downstream from the source agree with the assorted data remarkably well for a range of length scales extending over three orders-of-magnitude. It is concluded that results from application of the Lagrangian similarity hypothesis are significant for the laboratory modelling of diffusion in the atmospheric surface layer.

When the dimensions of a convective system in a saturated porous medium are sufficiently great, diffusion effects can be neglected except in regions where the gradients of fluid properties are very large. A boundary-layer theory is developed for vertical plane flows in such regions. In special cases, the theory is equivalent to that for laminar incompressible flow in a two-dimensional half-jet, or in a plane jet or round jet, for which similarity solutions are well known.

A number of experiments have been performed using a Hele-Shaw cell immersed in water, with a source of potassium permanganate solution located between the plates. At very small values of the source strength, a flow analogous to that of a plane jet from a slit is obtained. The distance advanced by the jet front, or cap, is measured as a function of time, and the velocity is found to be nearly proportional to the velocity of the fluid on the axis of the steady jet behind the cap, as given by the similarity law of Schlichting and Bickley. At large values of the source strength, a two-dimensional ‘broad jet’ of homogeneous solution descending under gravity is produced; the shape of the flow region can be calculated with little error from potential theory, neglecting the effect of the mixing layers.

A possible example of a mixing layer observed in a geothermal region is examined. The theoretical form of the temperature distribution is calculated numerically, taking into account the large viscosity variation with temperature and also the possibility of a large permeability variation. These effects are found to have less influence upon the solution than might have been expected. Quantitative values obtained for the physical parameters are consistent with other geophysical observations.

The mean velocity distribution in a low-speed three-dimensional turbulent boundary-layer flow was investigated experimentally. The experiments were performed on a large-scale model which consisted of a flat plate on which secondary flow was generated by the pressure field introduced by a circular cylinder standing on the plate. The Reynolds number based on distance from the leading edge of the plate was about 6 x 106.

It was found that the wall-wake model of Coles does not apply for flow of this kind and the model breaks down in the case of conically divergent flow with rising pressure, for example, in the results of Kehl (1943). The triangular model for the yawed turbulent boundary layer proposed by Johnston (1960) was confirmed with good correlation. However, the value of yuτ/v which occurs at the vertex of the triangle was found to range up to 150 whereas Johnston gives the highest value as about 16 and hence assumes that the peak lies within the viscous sublayer. Much of his analysis is based on this assumption.

The dimensionless velocity-defect profile was found to lie in a fairly narrow band when plotted against y/δ for a wide variation of other parameters including the pressure gradient. The law of the wall was found to apply in the same form as for two-dimensional flow but for a more limited range of y.

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 impingement of a rocket jet, exhausting into a vacuum, onto a solid surface is examined using the Newtonian approximation to analyse the transonic region. The jet exhaust into an unbounded vacuum required for this analysis is simplified as a quasi-radial flow using an exact calculation as a basis. Two examples are calculated giving the shock detachment distance and the ground pressures as a function of the rocket altitude.

An analysis of experimental results shows that the three most important terms in the energy balance of a mixing layer—the production, diffusion and dissipation terms—may be expressed in terms of an eddy viscosity, eddy diffusivity for turbulent energy, and a microscale, respectively, all being constant for a given cross-section. A first-order solution calculated for the resulting differential equation yields a turbulent intensity profile in qualitative agreement with experiment. The peak value of the turbulent intensity is found to depend on a dissipation constant and on the ratio of eddy diffusivity for turbulent energy to eddy viscosity. Experiments carried out with the intention of reducing turbulent intensities by means of extraneous vortices, generated by small delta wings, have shown slight increases in intensity, presumably because eddy viscosity increases with eddy diffusivity.

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.

The energy transfer due to non-linear interactions between the components of a gravity-wave spectrum discussed in Parts 1 and 2 of this paper is evaluated for a fully and partially developed Neumann spectrum with various spreading factors. The characteristic time scales of the energy transfer are found to be typically of the order of a few hours. In all cases the high frequencies and the low-frequency peak are found to gain energy from an intermediate range of frequencies. The transfer of energy to very low frequencies and to waves travelling at large angles to the main propagation direction of the spectrum is negligible. Computations are presented also for the rate of decay of swell interacting with local wind-generated seas (represented by a Neumann spectrum). An appreciable decay is found only for swell frequencies in the same range as those of the local sea.