Townsend (1954) has shown that turbulent vorticity may rotate and strain a diffusion wake, thereby increasing the contribution of molecular diffusion to the total mean dispersion over short diffusion times. To test whether any such effect occurs at longer diffusion times, the lateral dispersion of both helium and of carbon dioxide in air were measured downstream from a continuous point source in the turbulence produced by a grid in a wind tunnel. The data show that, for long diffusion times, accelerated molecular diffusion is negligible, so that molecular diffusion makes only an independent contribution to the total dispersion.

This article has a twofold purpose: (1) to analyse the available theoretical and experimental knowledge concerning flow in the inlet region of a smooth round tube, and (2) to point out that the e9 amplification factor method apparently predicts natural transition correctly over a significant fraction of the entire inlet lenght of the tube. The successful prediction indicates, but does not prove, that flow in a smooth round tube becomes turbulent at higher Reynolds numbers because transition occurs in the inlet lenght—not in the fully developed Poiseuille régime. The close agreement between theory and a test result obtained by Pfenninger indicates that the e9 method is valid for a wide variety of flows having x Reynolds numbers of transition ranging from 570,000 to 40 million. The results are applicable to both plane and axially symmetric flows.

In certain cases of steady motion of a conducting fluid in a magnetic field, the primitive equations may be integrated once, yielding a second-order partial differential equation in the stream function. This equation is highly non-linear in general, but for certain choices of basic flow and magnetic fields it is tractable. Several arbitrary functions of integration have to be evaluated to make the analysis useful. This may be done in a region that remains undisturbed. A short discussion is given to suggest a procedure for deciding in a special case whether this undisturbed region is ‘upstream’ or ‘downstream’.

Measurements of mean velocity, mean flow direction, normal turbulent stress in the direction of flow, and mean static pressure are reported for the subsonic flow field generated by identical twin jets of air issuing from parallel slot nozzles in a common wall and mixing turbulently with ambient room air. At the low nozzle velocity employed (72ft./sec), the two-dimensional plano-symmetric flow was effectively incompressible. Since the end walls prevented interjet air entrainment from the surroundings, a region of highly convergent flow was formed near the nozzles. In this region, contour maps clearly reveal (1) the sub-atmospheric static pressure through that accounts for the jet convergence, (2) a free stagnation point on the plane of symmetry, (3) stable symmetrical contrarotary vortices which recycle air on the concave side of each converging jet, and (4) the super-atmospheric static pressure mound that redirects the merging jet streams in a common downstream direction. Comparisons are made between the development of the flow, in both the region of jet convergence and the region of combined jet flow, and that of the single-jet counterpart which was previously reported.

When a sphere or other bluff body travels at supersonic speeds, a shock wave is formed close to the front surface. With increase of speed the air behind the shock is further compressed, and the shock wave moves closer to the surface. This paper considers the case where the region close to the stagnation point between the shock and the sphere can be taken to be a steady laminar boundary layer.

The approximate solution of the equations of motion follows closely the classical work of Homann (1936), ideas similar to those of Lighthill (1957) being used to apply it to the problem in hand. It consists mainly in reducing the equations to ordinary differential form by assuming forms of the flow variables which satisfy the boundary conditions, notably at the shock wave. In addition, several transformations are employed in order to simplify the equations and to increase the range of solutions, and also to facilitate the use of the ‘Mercury’ electronic computer in solving them.

The results give an insight into some aspects of hypersonic flows. Included in this paper are a selection of temperature and transverse velocity profiles across the boundary layer and several graphs relating such quantities as the shock stand-off distance and the skin-friction coefficient with Reynolds number. The last two mentioned are the most interesting. The first set gives the surprising result that the shock stand-off distance increases with increase in Reynolds number, whereas it is known that the skin-friction coefficient is inversely proportional to a decreasing power of the Reynolds number when it is lower than order 103, but the indication is that it tends to the expected constant power of ½ when the Reynolds number is of order 104.

The equations for planar two-dimensional steady flow of an ideal dissociating gas are linearized, assuming small disturbances to a free stream in chemical equilibrium.

As an example of their solution, the flow past a sharp corner in a supersonic stream is evaluated and the variations of flow properties in the relaxation zone are found. Numerical illustrations are provided using an ‘oxygen-like’ ideal gas and comparisons made with a characteristics solution. The flow past a sharp corner can be studied in a conventional shock tube and it may be possible to verify the present theory experimentally. In particular it may prove feasible to use the results to obtain a measure of the reaction rates in the gas mixture.

Approximate solutions are found for the fluid flow and heat transfer in a heated cylinder, closed at the bottom and opening at the top into a reservoir of cool fluid, which has been tilted at a small angle to the vertical.

One solution is found for large Rayleigh number when the boundary layer does not fill the tube, and another for small Rayleigh number when the boundary layer fills the tube. In both cases tilting causes a small increase in heat transfer which is proportional to the square of (l/a) tan ϕ, where l/a is the length–radius ratio and ϕ the angle of tilt.

An empirical relationship for the torque transmitted by fluid friction to an outer cylinder as a function of the angular velocity of the inner cylinder has been obtained by analysis of experimental data published by Wendt, Taylor and Donnelly. With one exception it is found that the torque G has the functional form $G = a \Omega^{-1}_1 + b\Omega ^{1 \cdot 36}_1,$ where Ω1 is the angular velocity of the inner cylinder and a and b are constants determined from the data. The formula applies to a range of values of Ω1 above the onset of instability extending to about 10 times the critical angular velocity. The experiments also show that the finite amplitude analysis recently advanced by Stuart gives the correct variation of torque over a short range above the critical speed. At speeds well beyond critical it is found that G varies approximately as Ω1.51, and that the variation of torque with gap width can be expressed as a simple power law with exponent about 0.31. In an appendix Dr G. K. Batchelor shows that these latter relations are consistent with the supposition that the flow is steady and consists of inviscid cores surrounded by boundary layers.

Cnoidal wave theory is appropriate to periodic waves progressing in water whose depth is less than about one-tenth the wavelength. The leading results of existing theories are modified and given in a more practical form, and the graphs necessary to their use by engineers are presented. As well as results for the wave celerity and shape, expressions and graphs for the water particle velocity and local acceleration fields are given. A few comparisons between theory and laboratory measurements are included.

A general numerical procedure is described whereby the details of the steady inviscid flow of a mixture of perfect gases about a blunt body, including the effects of finite dissociation and recombination rates, may be calculated. Several numerical examples are calculated in order to apply the numerical procedure to specific cases and also to show the effects of finite reaction times on the flow about a blunt body.

In this paper it is shown how earlier results for buoyant vortex rings may be extended to describe the corresponding two-dimensional case, which arises in the theory of bent-over plumes. It is again assumed that in uniform surroundings the circulation remains constant while the buoyancy acts to increase the momentum of the pair. The behaviour in two dimensions is quite different from that in three, however; a buoyant vortex ring spreads linearly with height, whereas a buoyant pair spreads exponentially with height, or linearly with time (and therefore, in a bent-over plume, linearly with distance downwind).

The theory has been extended to describe the rise of buoyant rings and pairs through stably stratified surroundings having a linear density gradient. The behaviour near the maximum height reached is found to depend critically in both cases on the relative rates at which the circulation and the momentum fall to zero. If these reach zero together, the rings or pairs will steadily increase in size and come to rest at a finite height and with a finite radius. If the circulation is non-zero when the momentum vanishes, the radius begins to decrease soon after the buoyancy becomes zero, and the vortices will therefore tend to break up suddenly and mix into their surroundings. There is a considerable increase in the final height which should be attained by vortex rings or bentover plumes if the initial circulation is increased; it is suggested that releasing smoke intermittently, rather than continuously, at high velocity might be a means of increasing the effective height of chimneys in calm conditions. When the circulation reaches zero before the momentum does, the solutions indicate that the radius becomes very large near the level of zero buoyancy.

The paper describes an experimental investigation of the pressures developed at the seat of collapse of cavities in water. Single transient cavities, generated by a spark discharge, are allowed to collapse on the end of a piezoelectric pressure-bar gauge which measures the variation of thrust with time. It is shown that both the peak force and duration of the cavity collapse pulse are functions of the cavity lifetime. From an estimate of the minimum radius attained by the cavity and the peak force, the peak pressure on collapse is found to be at least 10,000 atm. Streak schlieren photographs of the collapse process show that a shock wave is radiated into the water at the moment of collapse and that the cavity rebounds. At the collapse of the rebound cavities the pressures developed are comparable with those developed by the collapse of the initial cavity, and these probably contribute materially to cavitational surface damage.

Hydrodynamic stability of free boundary-layer flows is treated in general. It is found that the situations at low Reynolds numbers are universal for all velocity profiles of free boundary-layer type. Curves of constant amplification are calculated as far as O(R3). In particular, the asymptotic form of the neutral curves for R [eDot ] 0 is found to be α = R/(4√3), so that the critical Reynolds numbers of these flows are identically zero. The phase velocity of the disturbance is also found to be zero, for all disturbances, up to the second approximation.

A method of normalizing the velocity profiles is suggested, and existing results for the stability of various profiles at large Reynolds numbers are discussed from a new point of view.

The possibility exists of directly using the plasma, resulting from a controlled fusion reaction, to generate electricity by electromagnetic induction. Two special cases of a more general problem are considered here: (1)the extraction of optimum power from the steady one-dimensional flow of an incompressible inviscid plasma across a uniform transverse magnetic field in an externally loaded channel of arbitrarily varying cross-section, and (2) the extraction of optimum power from the steady one-dimensional flow of a compressible inviscid plasma across a uniform transverse magnetic field in a channel of uniform cross-section. In each case, the magnitude of the required external loading at optimum power operation is determined as a function of the parameters which characterize the hydromagnetic interaction. Also determined are the magnitudes of the terminal voltate, power, fluid mechanical to electrical conversion efficiency, and the variation of the fluid dynamical variables along the channel at optimum power.

A simple method is presented in this paper for calculating

1. the secondary velocities, and

2. the lateral displacement of total pressure surfaces (i.e. the ‘displacement effect’)

An electronic computer has been employed to calculate the ratio between the initial radii of curvature of the attached shock wave and the body for an axially symmetrical body in a uniform supersonic stream. The results are obtained with 4 exact digits for more than 200 cases. They extend results obtained previously (Cabannes 1951) by means of numerical integration.

The flow produced by an infinite rotating disk when the fluid at infinity is in a state of solid rotation is investigated numerically. When the fluid at infinity is rotating in the same sense as the disk, physically acceptable solutions exist in all cases. When the fluid at infinity is rotating in the opposite sense to that of the disk, the only physically acceptable solutions appear to be those in which there is a uniform suction present acting through the disk.

The hot-wire anemometer, used for recording speed variations in turbulent flow, involves in its working principle the unsteady heat transfer from a hot fixed surface to a fluctuating air stream moving past the surface. If the wire is maintained at a constant (high) temperature, the rate of loss of heat from the wire changes with the velocity of the incident stream, and the compensating rate of gain of heat, produced by the Joule heating effect of the electric current, changes, correspondingly. The accompanying change of current can be measured, and used to calculate the varying velocity of the air stream. The hot wire may have a diameter as low as 10−4 in. and the Reynolds number of the flow is then of the order of 0.05 for each ft. per sec of velocity. With low velocities, of the order of 10 or 20 ft./sec, the flow past the wire is in the range of small Reynolds number, and the exact equations of flow may be approximated by simpler equations in the manner of Oseen's theory (Lamb 1932). The approximate equations are not easy to solve when the flow is compressible, as it will be in the presence of the large temperature differences imposed by the heat of the wire. If, however, the temperature differences are assumed to be small, the approximate energy equation is no longer linked with the equations of continuity and momentum, and it may be solved without knowledge of the velocity field. The purpose of this note is to give the solution for the temperature field when a warm circular cylinder or a warm sphere is held at rest in a fluctuating stream.

The results of numerical calculations are presented for the motion of a bore over a uniformly sloping beach. The shallow water equations are solved in finite difference form, and a technique is developed for fitting in the bore at each step. The results are compared with the approximate formula given by Whitham (1958) and close agreement is found. The approximate theory is considered further here; the main addition is a rigorous proof that, within the shallow water theory, the height of the bore always tends to zero at the shoreline.