Investigations into the behaviour of the gas flowbehind spherical or cylindrical blasts have shown that secondary shocks arise within the original detonation gases. The secondary shock, at first weak, is carried outward with the expanding gases. Subsequently it strengthens and bends back toward the origin, arriving there with high intensity.

By using some recently developed techniques in shock dynamics and extending them where necessary, a theory is developed by which the motion of the main shock wave, as well as the formation and subsequent motion of the secondary shock, are given by explicit formulae. In addition, a method for determining, also by explicit formulae, the location of the contact surface between the detonation gases and the outside atmosphere is given. The results of a specific problem, which has been solved by numerically integrating the total equations of motion, and has also been checked experimentally, are compared with the results of the present theory.

It is shown that solitary hydromagnetic waves can propagate parallel to a uniform magnetic field in a cold collision-free plasma. These waves are exact solutions of the non-linear equations of motion except for the quasi-neutral approximation. The velocity of propagation lies in a range of values somewhat larger than the Alfvén velocity, and is of the order of 25 times the Alfvén velocity for hydrogen, the precise value depending upon the strength of the wave. Simple expressions exist for the velocities of the ions and electrons and the magnetic field inside the wave. The lines of force are spirals about the direction of propagation. The waves are symmetrical about their middle. The order of magnitude of their width is the geometric mean of the gyro-radii of the ions and electrons when moving with the Alfvén velocity. The maximum value of the magnetic field can be somewhat larger than the value away from the wave.

A new technique is described for measuring the axial mass flow rate in the turbulent jet formed when a gas in injected into a reservoir of stagnant air at uniform pressure. The jet is surrounded by a porous-walled cylindrical chamber, and air is injected through the wall until the pressure in the chamber is uniform and atmospheric, a condition which is taken to signify that the ‘entrainment appetite’ of the jet is satisfied.

Measurements made with the apparatus have allowed the deduction of an entrainment law relating mass flow rate, jet momentum, axial distance and air density, regardless of the injected gas, and including the effects of buoyancy. When the injected gas burns in the jet the entrainment rate is up to 30% lower than when it does not.

When rollers, placed horizontally and side by side so that each is half immersed in a tank of liquid, rotate in opposite directions, liquid is carried through the gap between them and divides to form a sheet over each roller. At low speeds the sheets are of uniform thickness across the width of the rollers, but at higher speeds they are regularly ridged owing to alternate increase and decrease in thickness. Preliminary observations led to the development of an approximate theoretical treatment of the even-flow régime and the critical conditions when the ribbed flow is about to begin. Results of this work are in full agreement with detailed experimental results.

On the assumption of (a) zero heat transfer, (b) unit Prandtl number, (c) linear viscosity temperature relation, and (d) small cross-flow, a correlation between a compressible laminar boundary-layer flow and an incompressible flow with different external conditions is established.

The correlation is applied to a known approximate method of solution for incompressible flow. For flow over a slender wing it is found that, so far as the effect on limiting streamlines—and hence on separation—is concerned, the fluid behaves as though it were incompressible but with pressure gradients multiplied by 1 + ½(γ − 1)M20 approximately, where M0 is the Mach number, supposed to be moderate in value. The effect on drag is also estimated.

An attempt is made to assess the effect of variable Prandtl number Pr, and it is found that the above multiplying factor must be replaced by 1+\frac {1}{2}Pr^{\frac{1}{2}}(\gamma - 1)M^2_0$1+\frac {1}{2}Pr^{\frac{1}{2}}(\gamma - 1)M^2_0$ but that variations in Prandtl number have little effect on the previous estimate of drag.

A method for measuring the interfacial structure between a co-current air-water flow using the absorption of light is described. Measurements of the root-meansquared displacement and the frequency spectrum are presented. The use of a Gaussian model to describe the interface is explored.

Incompressible slip flow past a semi-infinite flat plat at zero incidence is treated in terms of the linearized viscous flow equations. A formal solution is obtained using Fourier transforms and the Wiener-Hopf technique. Explicit inversion of the transform is not possible, but asymptotic expansions are discussed. These reveal the inadequacy of boundary-layer theory in predicting the nature of the solution, even at the plate surface. For example, the local shear forces on the plate are significantly different from boundary-layer values, even far downstream, where slip effects are small. The boundary-layer limit is approached as the Reynolds number based on the mean free path or, equivalently, the free-stream Mach number tends to infinity.

In turbulent flow past rigid boundaries, there can be distinguished regions close to the wall in which the local rates of energy production and dissipation are so large that aspects of the turbulent motion concerned with these processes are determined almost solely by the distribution of shear stress within the region and are independent of conditions outside it. These regions are here called equilibrium layers because of the equilibrium existing between local rates of energy production and dissipation. Three kinds of equilibrium layer have been studied experimentally, the constant-stress layer, the transpiration layer and the zero-stress layer, but there are other possible forms. One that is of importance in the theory of self-preserving flow in boundary layers and in diffusers is the ‘linear-stress’ layer in which the stress increases linearly with distance from the wall. The properties of these various equilibrium layers are considered and the distributions of mean velocity are derived from the equation for the turbulent kinetic energy and certain assumptions of flow similarity.

The theory of self-preserving wall flow, usually expressed as a combination of the law of the wall and the defect law, assumes compatibility between the outer flow and the equilibrium layer, and the course of development depends on the kind of equilibrium layer. Earlier work by the author, which assumed the defect law, is only valid if the whole of the equilibrium layer is a constant-stress layer and this is not true in strong adverse pressure gradients. A consistent theory is developed for these flows by assuming a ‘linear-stress’ layer, and the solutions show the relation between flows of finite stress and of zero stress and provide a plausible explanation of the phenomenon of downstream instability observed by Clauser. Self-preserving flow in wedges is treated on similar lines.

The flow of an inviscid, incompressible electrical conducting fluid in a channel of constant rectangular cross-section is considered, when the flow enters a region which contains a magnetic field transverse to the flow and electrodes on opposite sides of the channel. This geometry is typical of a d.c. induction pump or magnetohydrodynamic generator. The conducting fluid external to the magnetic field acts as a shunt and produces a non-uniform electric potential field and hence a non-uniform Lorenz force on the fluid, and causes the fluid velocity profile to be distorted. These effects are calculated theoretically for small magnetic Reynolds number and small magnetic interaction parameter. It is found that the velocity at the centre-line of the channel is retarded and at the walls the velocity is accelerated. The fractional change of velocity at the wall is equal to approximately 0·44 times a modified magnetic interaction parameter.

The force on a sphere moving through an inviscid, conducting fluid in the presence of a uniform magnetic field B0 is calculated for the low-conductivity case where the hydrodynamic motion deviates only slightly from potential flow. The magnetic Reynolds number is assumed small. The force on the sphere is found to consist of both a drag and a deflective component which tends to orient its motion parallel to a magnetic field line; if the sphere's velocity is V, the force may be written \bf {R} = -AB^2_0\bf {V} + \bf C(V.B_0)B_0$\bf {R} = -AB^2_0\bf {V} + \bf C(V.B_0)B_0$ where the coefficients A and C depend on the conductivities of both sphere and fluid. The coefficients are evaluated by calculating the Joule dissipation for particular orientations of V relative to B0. In one case the force is also calculated directly from the perturbed pressure distribution in the fluid. In an analogous way, a spinning sphere in a conducting fluid experiences both resistive and gyroscopic torques.

Expressions in closed form are derived for a number of local properties of a random, irrotational wave field. They are: (i) the mean potential and kinetic energies per unit projected area; (ii) the energy balance among the processes of energy input from the surface pressure fluctuations, rate of growth of potential and kinetic energy and horizontal energy flux; and (iii) the partition between potential and kinetic energy. These expressions are mainly in terms of quantities measured at the free surface, which are therefore functions of only two spatial variables (x, y) and of time t.

Approximations for these expressions can be found simply by subsequent expansion methods; the fourth order being the highest for which the assumption of irrotational motion is appropriate in a real fluid. It is shown that the mean product of any three first-order quantities is of fourth or higher order in the root-mean-square wave slope, and this result is applied in estimating the magnitude of some higher order effects. In particular, the skewness of the surface displacement is of the order of the root-mean-square surface slope, which has been confirmed observationally by Kinsman (1960).