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.

The vapour-screen method of flow visualization in supersonic wind tunnels is outlined, and the development of a suitable technique for use in the 3 ft. tunnel at R.A.E. Bedford described, together with the associated optical and photographic equipment.

The results of tests to determine the humidity required to produce an optimum density of fog in the working section over the Mach number range 1.3–2.0 are presented and the influence of tunnel pressure and temperature discussed. Numerous vapour-screen photographs of the flow over and behind delta wings are included and some comparisons made with the corresponding surface oil-flow patterns.

The process of condensation, the physical and optical properties of the resulting fog, and the formation of the vapour-screen picture are all considered in some detail.

The effects of humidity on the Mach number and static pressure in the working section were investigated and the results are compared with theoretical estimates at a nominal Mach number of 2.0. It is shown that the adverse effects of condensation on the flow at high Mach numbers may be alleviated by the use of liquids with a lower latent heat of evaporation than water, and some results obtained at a Mach number of 2.0 using carbon tetrachloride vapour are described.

The possibility of extending the vapour-screen technique to transonic and subsonic speeds is also considered, and some results obtained at a Mach number of 0.85 are included.

A solution is obtained for the motion of a thin oil sheet, of non-uniform thickness, under a boundary layer. The following points are deduced: (a) The oil flows in the direction of the boundary-layer skin-friction, except near separation, where the oil tends to indicate separation too early. These conclusions are independent of oil viscosity. (b) The effect of the oil flow on the boundary-layer motion is very small.

The application of the results to the interpretation of oil-flow patterns is briefly considered.

A study was made of the laminar-turbulent transition of a wake behind a thin flat plate which was placed parallel to a uniform flow at subsonic speeds. Experimental results on the nature of the velocity fluctuations have made it possible to classify the transition region into three subregions: the linear region, the non-linear region and the three-dimensional region.

In the linear region there is found a sinusoidal velocity fluctuation which is antisymmetrical with respect to the centre-line of the wake. The frequency of fluctuation is proportional to the $\frac {2}{3}$ power of the free-stream velocity, and the amplitude increases exponentially in the direction of flow. The behaviour of small disturbances in the linear region was investigated in detail by inducing velocity fluctuation with an external excitation—actually sound from a loudspeaker. Solutions of the equation of a small disturbance superposed on the laminar flow were obtained numerically and compared with the experimental results. The agreement between the two was satisfactory.

When the amplitude of fluctuation exceeds a certain value, the growth rate deviates from being exponential due to non-linear effects. Although velocity fluctuations in the non-linear region are still sinusoidal and two-dimensional, the experimental results on the distributions of amplitude and phase indicate that the flow pattern may be described by the model of a double row of vortices. This configuration lasts until three-dimensional distortion takes place in the final subregion, the three-dimensional region, in which the fluctuation loses regularity and gradually develops into turbulence without being accompanied by abrupt breakdown or turbulent bursts.

The effect of viscous dissipation and applied magnetic field is investigated for the case of the fully developed natural convection of a fluid between two heated walls. When electrical and viscous dissipation is negligible, short-circuited Hartmann flow results. The deviation of the velocity and temperature profiles from those existing in Hartmann flow are presented for various Hartmann numbers when dissipation is not neglected. It is shown that increasing the applied magnetic field rapidly decreases the influence of both viscous and joulean dissipation on the velocity and temperature profiles.

The method of characteristics is used to calculate numerical solutions for the one-dimensional motion of a plane shock-wave through a stationary gas which contains a region of non-uniform density. These solutions are compared with those given by the Chisnell-Whitham approach which ignores the effects on the shock-wave of the disturbances which are generated in the flow behind it, and also with the asymptotic solution given by the simple theory which regards the nonuniform region as a contact-surface discontinuity. It is concluded that the results of the simplified theories must be applied with caution.

The behaviour of a natural convection plume above a line fire is studied both theoretically and experimentally. In the theoretical treatment, a turbulent plume above a steady two-dimensional finite source of heated fluid in a uniform ambient fluid is investigated. By the use of the lateral entrainment assumption, a quadrature solution has been obtained for each of two separate ranges of a source Froude number, F < 1 or F > 1. In neither of these cases can the finite width line source be accurately represented by an equivalent mathematical line source at a lower level. Only the special case, F = 1, can be so represented and its solution is discussed.

In the experimental treatment, hot gases, resulting from the burning of a liquid fuel in a long channel burner, are driven upwards by buoyancy and gradually cooled down by the entrainment of ambient air. The average temperature along lines parallel to the channel burner was measured by a piece of resistance wire. For the case of a non-luminous diffusion flame, the effective radiation loss to the surroundings was assumed to be negligible, and,by a comparison of the energy flux supplied from the fuel and the energy flux contained in the plume, the characteristic turbulence entrainment coefficient is determined. By the alternate use of either an absorbing or a reflecting surface for the table-top surrounding a luminous flame, a measurement was made of the energy radiated from the flame that was intercepted by the fire surroundings and subsequently returned to the buoyancy plume by heating the ingested air. These measurements agree with estimates computed from such data as are available. The experimental results relating to the behaviour of the convection plume agree closely with the theoretical predictions in all cases.

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.

Isolated masses of a dense aqueous solution (i.e. thermals) were released at the surface of a freshwater layer overlying one of salt water. While the whole of a thermal remained in the upper layer, the equations $z = n_1r, \; z^2 = k_1t$, with $k_1 = C_1 n_1^{\frac {3}{2}}(Mg| \rho)^{\frac {1}{2}}$, were obeyed, where z is the distance travelled, 2r the width of the thermal, t the elapsed time, M the mass excess (the difference between the masses contained within and displaced by the thermal while in the upper layer), and ρ the density of the displaced fluid. n1 was constant for any one thermal, but varied between thermals over the range 1·9 to 7·5. C1 had roughly the same value (0·73) for all thermals.

The behaviour after the leading extremity of the thermal (the ‘front’) entered the lower layer depended on the value of the parameter S = Vρ/M, where Δρ is the density difference between the upper and lower layers and V is the volume of the thermal when the widest part is at the level of the discontinuity. It was found that Y = 0 if S = β (‘weak’ thermals), and Y = 0·95−½S if 0·1 < S [les ] β (‘strong’ thermals), where Y is the fraction of the mass of the substance released which penetrated indefinitely into the lower layer. The constant β was approximately equal to 1.90.

In weak thermals, the equation z − s = a1(t − ts)2 was obeyed while the front was in the lower layer, until the cluminating point z = s was reached at t = ts. The acceleration a1 was always negative, and constant for any one thermal, but varied between thermals. Also for weak thermals, $x = C_2 V^{\frac {1}{3}}|S$, where x is the distance from the interface to the culminating point and C2 is a constant. C2 was approximately equal to 3·5. For strong thermals, the distance travelled while the front was in the lower layer obeyed the equation z2 = k2t. The origins of z and t usually differed from those found in the upper layer, and generally k2 ≠ k1.

A slender-body theory for the flow past a slender, pointed hydrofoil held at a small angle of attack to the flow, with a cavity on the upper surface, has been worked out. The approximate solution valid near the body is seen to be the sum of two components. The first consists of a distribution of two-dimensional sources located along the centroid line of the cavity to represent the variation of the cross-sectional area of the cavity. The second component represents the cross-flow perpendicular to the centroid line. It is found that over the cavity boundary which envelops a constant pressure region, the magnitude of the cross-flow velocity is not constant, but varies to a moderate extent. With this variation neglected only in the neighbourhood of the hydrofoil, the cross-flow is solved by adopting the Riabouchinsky model for the two-dimensional flow. The lift is then calculated by intergrating the pressure along the chord; the dependence of the lift on cavitation number and angle of attack is shown for a specific case of the triangular plan form.

The paper considers the flow of an incompressible, viscous, perfectly conducting fluid past a fixed obstacle in the presence of an applied magnetic field which is parallel to the stream at large distances from the obstacle. A simple transformation of the fluid velocity and the total head enables the magnetohydrodynamic flow past the obstacle to be determined from the corresponding flow of a nonconducting fluid past the same obstacle but with a reduced main-stream velocity. The method is illustrated by considering the flows past a sphere, a circular cylinder and a semi-infinite flat plate for different field strengths. The drag on the sphere is plotted as a function of the field strength for a fixed Reynolds number. The patterns of the flow past a circular cylinder are sketched and an inference is made to the way in which disturbances can propagate upstream for the case when the main-stream velocity is less than the Alfvén speed. These give rise in the first instance to a separation bubble upstream of the cylinder. Finally the range of applicability of familiar high Reynolds number approximations to magnetohydrodynamic flows is discussed. In particular, if the main-stream velocity is equal to the Alfvén speed, the boundary-layer approximation is shown to be no longer valid.

The effect of combustion or heating on a slightly non-uniform flow in a tube of constant radius is explored by examining a simplified model, in which a density decrease occurs across a plane actuator-disk normal to the axis of the tube. The flow is considered to be steady, axi-symmetric, incompressible and inviscid and to originate at an injector-plate which is situated upstream of the disk. This paper analyses and discusses the effects caused by the density decrease when the velocity of flow through the injector-plate has a fractional non-uniformity ue, when there is a curvature θe, of the injector-plate, and when the density decrease has a fractional non-uniformity δ2. It is shown that the non-uniformity of the flow far downstream of the disk caused by the disturbances ue and θe is diminished by the density decrease; while that due to the disturbances δ2 is increased, unless the density decrease occurs close to the injector-plate. The distance separating the injector-plate and actuator-disk is found to be an important parameter. When this distance is small, compared to the radius of the tube, and the density decrease is severe, a small disturbance ue, θe or δ2 may set up a pressure variation at the injector-plate of many times the inlet dynamic pressure of the flow. It is conjectured that this pressure variation could affect the uniformity of velocity and composition of the flow through the injector-plate, and thus cause the disturbances ue and δ2 to grow or diminish.

The mean position of the cylinder is in the mean free surface, and the cylinder is oscillating vertically (heaving) with a simple harmonic motion of small amplitude. The problem is studied both theoretically and experimentally. The present paper may be regarded as a sequel to an earlier paper (Ursell, Dean & Yu 1959) on the waves due to a piston wave-maker.

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.

In the flow past a slender delta wing at incidence one can observe a roughly axially symmetric core of spiralling fluid, formed by the rolling-up of the shear layer that separates from a leading edge. The aim in this paper is to predict the flow field within this vortex core, given appropriate conditions at its outside edge.

The basic assumptions are (i) that the flow is continuous and rotational, and (ii) that viscous diffusion is confined to a relatively slender subcore. In addition it is assumed that the flow is axially symmetric and incompressible. Together, these admit outer and inner solutions for the core from the equations of motion. For the outer solution the subcore is ignored, and the flow is taken to be inviscid (but rotational) and conical. The resulting solution consists of simple expressions for the velocity components and pressure. For the inner solution, which applies to the diffusive subcore, the flow is taken to be laminar, and certain approximations are made, some based on the boundary conditions and some analogous to those of boundary-layer theory. The solution obtained in this case is a first approximation, and has been computed.

A sample calculation yields results which are in good qualitative and fair quantitative agreement with experimental measurements.

The velocity potential for a simple source moving in a straight line at constant depth in a two-layer ocean is obtained by the Fourier transform method. It is used to develop a formula for the wave-making resistance of a ‘thin’ ship for both surface and internal waves. An asymptotic expansion is used to delineate quantitatively the internal wave system. It is shown that at speeds less than the critical speed transverse and divergent wave systems are excited, while at speeds greater than the critical internal wave speed only the divergent wave system is excited. Examples of the shape of wave crests and of wave heights are given.

Local solutions are found for the inviscid shear flow past an acute corner (of included angle [les ] ½π on the side of the fluid) on an otherwise arbitrary boundary. Unlike irrotational ‘corner flows’, these solutions are determinate locally, provided that the vorticity is known. Under certain circumstances the existence of a corner eddy may be inferred.

The existence of steady, one-dimensional, finite-amplitude waves in a cold collison-free plasma is investigated for the case in which the plasma and the magnetic field are uniform far ahead of the wave. It is supposed that the magnetic field at infinity is inclined at an angle β to the direction normal to the plane of the waves (0 [les ] ½π). It is shown that the problem is equivalent to determining the orbits of a particle in a uniformly rotating field of force.

Two types of waves are found to exist for β ≠ 0: solitary waves and quasishocks. In a quasi-shock, the plasma and magnetic field oscillate irregularly behind the wave front about mean values, which are different from the values ahead of the wave. The width of the wave front is of the order of the ion gyroradius. The quasi-shocks resemble oblique magnetohydrodynamic shock-waves. For the case β = 0, only solitary waves exist, which have already been described (Saffman 1961).

The stability of the waves is considered, and it is concluded that the quasishocks are stable but that the solitary waves for β ≠ 0 are unstable.

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 $1+\frac {1}{2}Pr^{\frac{1}{2}}(\gamma - 1)M^2_0$ but that variations in Prandtl number have little effect on the previous estimate of drag.