Small regions in a flow where the density is different from that of the surrounding gas do not exactly follow accelerated motions of the latter, but move faster or slower depending on whether their density is smaller or larger than that of the main flow. This behaviour cannot be quantitatively explained by treating a gas ‘bubble’ as a hypothetical solid particle of the same density, because a gas bubble cannot move relative to the surrounding gas without being transformed into a vortex which absorbs part of the energy of the relative motion.

To illustrate the acceleration effect, the flow velocity behind known pressure waves in a shock tube is compared with the observed velocity of a bubble produced by a spark discharge. The displacement of such a bubble by a wave exceeds that of a flow element by more than 20%, but the bubble density is not known. If the spark discharge is replaced by a small jet of another gas, a pressure wave cuts off a section of this jet which then represents a bubble of known density.

A theory is developed which permits computing the response of such bubbles to accelerations. The ratio of the bubble velocity to the velocity of the surrounding gas depends on the density ratio for the two gases and on the shape of the bubble, but not on the acceleration. Experimental results with H2, He, and SF6 bubbles in air, accelerated by shock waves of various strength, are presented and agree well with the theoretical predictions. The results apply regardless of whether accelerations are produced by pressure waves in a non-steady flow or by curvature of streamlines in a steady flow. Various aspects of the experimental observations are discussed.

The instability of the accelerated interface between a liquid (methanol or carbon tetrachloride) and air has been investigated experimentally for approximate sinusoidal disturbances of wave-number range from well below to well above the cut-off. The growth rates are measured and compared with theoretical results. A third-order theory shows the phenomena of overstability which is found in the experimental results. Some measurements of later stages of growth agree moderately well with the available theory and disclose some additional phenomena of bubble competition, Helmholtz instability with transition to turbulence, and jet instability with production of drops.

This paper is concerned with the dispersion of a material quantity in the steady flow of a viscous fluid through a random network of capillaries (which is a useful model of a porous medium), for the case in which molecular diffusion and macroscopic mixing, due to the randomness of the streamlines, are both important. A Lagrangian correlation function is introduced and the longitudinal and lateral effective diffusivities are thereby calculated for all values of Ul/κ less than some large value. Here, l denotes the length of a capillary, U the mean velocity of the fluid, and κ the molecular diffusivity of the material quantity. The theory is compared with experimental observations of dispersion in flow through granular beds.

When a body moves through a stratified fluid, i.e. one whose density decreases upwards, gravity waves are set up and this causes a resistance to motion. An axisymmetric case is considered in which a body moves steadily and vertically through a fluid whose density decreases exponentially upwards. The fluid is supposed perfect, incompressible, and unbounded in all directions. The equations of motion are linearized, and with a fairly general initial motion of the surrounding fluid, the limit of the solution as t → ∞ is evaluated. Transform methods are used to solve the equation of motion, and the methods of steepest descents and stationary phase are used to obtain approximate solutions.

Streamlines and the distortion of the constant density levels for a spindle-shaped body are shown. The curves of resistance against a function of the velocity for the circular cylinder, the sphere, and a spindle-shaped body are also given. A criterion is given for when the maximum wave resistance for a sphere may be expected, and an estimate of this maximum resistance is made.

It is shown that in Stokes's flow the perturbation field, due to the addition of one more sphere to a shear flow of a fluid containing a number of non-interacting spheres, has the property that the total additional shearing force, acting on any plane normal to the direction of velocity change, is zero. However, the perturbation velocity, integrated over such a plane, takes a constant value, positive if the plane lies on one side of the sphere and negative if it lies on the other side. It follows that the effect of all the spheres is not to alter the shearing stress at all, but to reduce the mean shear by a factor 1 – 2·5c, where c is the concentration. This suggests that Einstein's viscosity law should be altered to η = η0/(1 – 2·5c) when c is not small.

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.

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.

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.

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.