A two-dimensional free-jet water tunnel developed at the St Anthony Falls Hydraulic Laboratory of the University of Minnesota is described briefly. Results of experimental measurements on a two-dimensional cup, symmetrical wedges, inclined flat plates, and a circular cylinder in the tunnel are given.

Measured force coefficients at zero cavitation number are in good agreement with theory. Shapes of the cavities were computed for one of the wedges and for one of the plates at zero cavitation number; the observed shapes are also in good agreement with the theory.

For non-zero cavitation numbers, theoretical results for force coefficients were available for comparison in only two cases. For one of these, the cup, agreement between theory and experiment was good up to a cavitation number of about 0.5. For the other, a symmetrical wedge, experimental results were compared with a linear theory with good agreement for cavitation numbers between about 0.1 and 0.3. In the case of the wedge, measured cavity lengths were somewhat shorter than predicted by the linear theory. All other comparisons with theory at non-zero cavitation number had to be made with the theory as developed for infinite fluid. The experimental force coefficients were less than predicted by infinite-fluid theory, but tended to approach the theoretical values as the cavitation number increased. A similar tendency marked the comparison between the experimental data and data taken by others in closed tunnels.

The steady, two-dimensional flow through an arbitrarily-shaped gauze, of non-uniform properties, placed in a parallel channel is considered for the case in which viscosity can be ignored except in the immediate vicinity of the gauze. The equations are linearized by requiring departures from uniformity both in the flow and in the gauze parameters to be small. Knowledge of any three of the upstream profile, the downstream profile, the shape of the gauze and the gauze parameters, allows the other to be calculated from a linear relation between these four quantities. Particular solutions are given for the production of a uniform shear and the flow through linear and parabolic gauzes. The validity of the solution is verified by experiment. It is shown that the method can also be applied to two-dimensional flow in a diverging channel, axisymmetric flow in a circular pipe and in a circular cone and to flow through multiple gauzes.

This paper gives the extension of the approximate theory developed in Part 1 (Whitham 1957) to three-dimensional problems. The basic equations are derived in §1, using the original assumption of a functional relation between the strength of the shock wave at any point and the area of the ray tube. An analogy with steady supersonic flow is found. For the diffraction of a plane shock wave by an obstacle, the equations and boundary conditions are exactly the same as those for steady supersonic potential flow past that obstacle, with a special choice of the density-speed relation. The successive positions of the shock wave are the equipotential surfaces of the supersonic flow. The 'shock-shocks’ introduced in Part 1, i.e. discontinuities in the slope and Mach number of the shock wave, correspond to the steady oblique shock waves in the supersonic flow problem. They arise when Mach reflexion occurs.

In §2 the theory is applied in detail to the diffraction of a plane shock wave by a cone. Then, in §3, a small perturbation theory is applied to the two typical problems of (i) diffraction by a slender axi-symmetrical body of general shape, and (ii) the stability of a plane shock. Many further applications would be possible and some brief comments on these are made in §4.

This paper is concerned with the propagation of small initial disturbances in a conducting gas under the influence of a uniform external magnetic field.

For a perfect conductor, there are three types of plane waves, each of which depends strongly on the angle at which the magnetic field is crossed. The modifying effects of finite conductivity are determined and, in the case of these waves, this is done uniformly for all angles. A general disturbance may be resolved into two parts, one of which satisfies a fourth-order equation and the other a fifth; for a perfect conductor these reduce to second-and fourth-order equations, respectively.

The free oscillations of the gas are examined when it is contained in a rectangular box, and, in particular, when the external field is very weak or very strong. For vanishingly weak fields the idealization of infinite conductivity proves to be inadequate. Finally, the initial-value problem is discussed.

When a rotating layer of fluid is heated uniformly from below and cooled from above, the onset of instability is inhibited by the rotation. The first part of this paper treats the stability problem as it was considered by Chandrasekhar (1953), but with particular emphasis on the physical interpretation of the results. It is shown that the time-dependent (overstable) motions occur because they can reduce the stabilizing effect of rotation. It is also shown that the boundary of a steady convection cell is distorted by the rotation in such a way that the wave length of the cell measured along the distorted boundary is equal to the wavelength of the non-rotating cell. This conservation of cellular wavelength is traced to the constancy of horizontal vorticity in the rotating and non-rotating systems. In the finite-amplitude investigation the analysis, which is pivoted about the linear stability problem, indicates that the fluid can become unstable to finite-amplitude disturbances before it becomes unstable to infinitesimal perturbations. The finite-amplitude motions generate a non-linear vorticity which tends to counteract the vorticity generated by the imposed constraint of rotation. Under experimental conditions the two fluids, mercury and air, which are considered in this paper, will not exhibit this finite amplitude instability. However, a fluid with a sufficiently small Prandtl number will become unstable to finite-amplitude perturbations. The special role of viscosity as an energy releasing mechanism in this problem and in the Orr-Sommerfeld problem suggests that the occurrence of a finite-amplitude instability depends on this dual role of viscosity (i.e. as an energy releasing mechanism as well as the more familiar dissipative mechanism). The relative stability criterion developed by Malkus & Veronis (1958) is used to determine the preferred type of cellular motions which can occur in the fluid. This preferred motion is a function of the Prandtl number and the Taylor number. In the case of air it is shown that overstable square cells become preferred in finite amplitude, even though steady convective motions occur at a lower Rayleigh number.

If an electric current of uniform density j0 is passed axially through a stationary fluid between concentric cylinders of radii r1 and r2 (> r1), the fluid is stable to axisymmetric disturbances only if the damping provided by viscosity and electrical resistivity is sufficiently large. It is shown herein that the fluid may also be stabilized by passing a line current J along the axis, sufficient conditions for stability being $J \le -\pi j _0(r^2_2 - r^2_1)$, or $\ge J\; \pi j _0r^2_1$

The values of J needed to stabilize the fluid when the fluid has non-zero viscosity and finite conductivity are calculated for the case r2-r1 [Lt ] r1. In this latter case, the ring vortices which exist under conditions of neutral stability are exactly the same as those for flow between rotating cylinders if J and j0 have the same sign, and if J is not very small compared with πj0r2.

The supersonic flow field outside a leading edge separation bubble has been computed in detail by a special application of the method of characteristics. Experimental observations on a two-dimensional square-nosed flat plate at M = 1·96 formed the initial data, and base points were established on the plate surface. Computations proceeded outwards and upstream to the sonic line and bow wave, the bow wave entropy gradient being taken into account. The shape of the sonic line was found to be very sensitive to the conditions along the plate surface. Streamlines and iso-Mach lines have been interpolated and are presented. Good agreement was found at the intersection of the network and the bow wave between computed values and those given directly by the shock wave equations. A comparison has been made with interferometric results from France.

Exact transfer calculations for boundary layers with longitudinal pressure gradients are very complicated, but in the literature several approximate methods are known for the rapid calculation of both the wall friction and the heat transfer. A ‘wedge method’ propounded by Meksyn turns out to be one of the most rapid methods, being no less accurate than other approximate methods. A way of refining this method is proposed.

This paper also shows that asymptotic expansions provide convenient relations which are capable of expressing the Nusselt number explicitly in terms of the Prandtl number.

It is shown that, together with the asymptotic expansions, Meksyn's method permits rapid calculation of local heat transfer numbers. Some examples of application are given for elliptical cylinders and spheres for several values of the Prandtl number.

A physical theory is proposed for the skin friction on a flat plate at zero incidence in the transition flow regime, i.e. in the flow of a moderately rarefied gas. The ratio of the molecular mean free path to the characteristic size of the plate is assumed of order unity or larger. A general formula for the perturbation to the well-known friction of the free-molecule theory is given. This perturbation is attributed to the intermolecular collisions which are neglected on the basis of the free-molecule hypothesis. The expected rate of collisions are calculated for rigid spheres, using the classical kinetic theory.

Although this is intended as an approximate theory, the theoretical results check surprisingly well with the limited experimental data that are available. The present theory shows that the ratio of the Reynolds number to the Mach number squared is the governing parameter for determining the intermolecular collision effect on skin friction in the transition flow regime.