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.

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 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 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.

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.

Induced magnetic fields in shock-tube flows have been measured by previous authors, in order to determine the electrical conductivity of ionized gases. Distortion of the applied magnetic field was taken to be small. In the present work, the full magnetic field solution is developed for idealized boundary conditions. At a magnetic Reynolds number equal to 4 the distortion is found to be considerable, but the field is well represented by a solution correct to third order in magnetic Reynolds number. The axial field in a real shock-tube configuration was computed, and experimentally measured fields were found to agree reasonably with theory.

The effects of heat-capacity lag on the flow over slender bodies are examined by means of an extension of Ward's (1949) generalized treatment of the slender-body problem. The results are valid for smooth bodies of arbitrary cross-sectional shape and attitude in the complete Mach number range up to, but not including, hypersonic conditions. Transonic flow can be treated owing to the presence of a dissipative mechanism in the basic differential equation, but the results in this Mach number range are probably of limited practical value.

The results show that cross-wind forces are unaffected to a first approximation, but that drag forces comparable with laminar skin-friction values can arise as a result of the relaxation of the internal degrees of freedom. The magnitude and sign of these effects depend strongly on body shape and free-stream Mach number.

Results are given for the surface pressure coefficient, and the variations of translational and internal mode temperature on and near the body are also found. The influence of these latter effects on heat transfer to the body is discussed.

Let D0 be the Stokes drag on an arbitrary body moving parallel to a principal axis of resistance, with velocity U, through an unbounded fluid. The Oseen drag, D, experienced by this same body moving with equal velocity and identical orientation through the unbounded fluid is then given by the expression $\frac {D}{D_0} = 1 + \frac {D_0}{16 \pi \mu c U} R + O(R^2)$ where c is any characteristic particle dimension and $R = cU \rho|\mu$ is the particle Reynolds number. An analogous expression is given for the case where the motion is not parallel axis. Finally, an expression is given for the Oseen resistance of an arbitrary falling parallel to a principal axis of resistance along the axis of a cylindrical tube of finite radius.

A solution is given for a viscous vortex in an infinite liquid. Similarity arguments lead to a reduction of the equations of motion to a set of ordinary differential equations. These are integrated numerically. A uniform feature is the constant circulation K outside the vortex core, which is also a viscous boundary layer. The circulation decreases monotonically towards the axis. The axial velocity profiles and the radial velocity profiles have several characteristic shapes, depending on the value of the non-dimensional momentum transfer M. The solution has a singular point on the axis of the vortex. The radius of the core increases linearly with distance along the axis from the singularity, and, at a given distance, is proportional to the coefficient of viscosity and inversely proportional to K.

Finally, a discussion is given to indicate that intense vortices above a plate, like the confined experimental vortex, or above the ground, like the atmospheric tornado and dust whirl, will not resemble the theoretical vortex except, possibly, far above the plate.

The effect of turbulence on an applied magnetic field is considered in the case when the magnetic Reynolds number Rm is large compared with unity but small compared with the ordinary Reynolds number R of the turbulence. When the applied field is sufficiently weak, it is argued that its effect on the velocity field is negligible. The equation for the field is then linear and its spectrum may be obtained throughout the equlibrium range of wave-numbers. It appears that the spectrum increases as $k^{\frac {1}{3}}$ up to a wave-number kc marking the threshold of conduction effects, and falls off as $k^{-\frac {11}{3}}$ beyond kc. The net effect of the turbulence is expressed in terms of an eddy conductivity equal to $R_m^{- \frac {5}{2}}$ times the electrical conductivity of the fluid. The effect of magnetic forces when these are not negligible is also tentatively considered.