A programme of shock tube experiments has been conducted to study the refraction of plane shock waves at interfaces between two gases. Shocks of strength ζ = 0·85 (weak) and ζ = 0·30 (fairly strong) were allowed to impinge, at various angles of incidence, on interfaces between air/CO2 and air/CH4, and the resulting configurations were photographed through a Mach-Zehnder interferometer. From the interferograms, measurements were made of the strengths of the reflected waves, and of the angles of refraction, and the values were compared with the theoretical calculations of Polachek & Seeger (1951). Within the range of parameters for which the refraction model assumed by the theory is applicable–the so-called ‘regular refraction’ region–the observations were in excellent agreement with the theoretical predictions.

When the study was extended to ranges of the parameters for which the theory is clearly inadequate, a succession of rather complex ‘irregular refraction’ patterns was observed. Although these configurations were highly interesting qualitatively, each of them involved curved shocks, non-uniform regions of flow, and other less simple processes which discouraged any formal theoretical analysis. On a less rigorous basis, however, it could be shown that these patterns were internally consistent, and that each represented a distortion of a regular refraction process which was reasonable under the prevailing aerodynamic conditions.

Certain observations in these refraction experiments appear to be of some significance outside the specific problem. (i) The sensitivity of strong shock refractions to the values of the specific heat ratio λ for the two gases suggests a possible technique for the measurement of λ and its temperature dependence. (ii) Two of the irregular refraction patterns display a transition process which would be equally appropriate to the onset of the Mach configuration in the shock reflection problem. (iii) Some irregular refractions can be considered as special cases in the problem of the interaction of a shock and a boundary layer.

This paper considers the flow at high Mach number behind the curved shock formed when a supersonic stream impinges on an axisymmetrical body with a rounded nose.

The solution is obtained as a double expansion in $\delta = (\gamma -1)|(\gamma +1),$ where γ is the adiabatic index, and M−2; the expansion is developed to within terms of order (δ+M−2)3.

Expressions are obtained for the distance between the body and the shock, the radius of curvature of the shock compared with that of the body, and the pressure distribution on the body.

An inequality is demonstrated involving the rate of production S of mean-square vorticity in isotropic turbulence and a factor γ which may be said to allow for intermittency or for the non-vanishing of fourth-order cumulants. An extreme state, corresponding to equality of this relationship, occurs if S = 0·64 and γ = 2·14. The experimental values are S = 0·4 and γ = 4. Another kinematical relation shows that the mechanism of vorticity production resembles collision between fluid particles rather than the swirling of contracting jets.

Two concentric spheres are supposed to rotate about the same axis with almost the same angular velocity, so that the viscous stresses over the surfaces of the spheres induce a flow which may be represented by a small perturbation superimposed upon a rigid body rotation of the fluid as a whole. The governing equations are therefore linearized in the magnitude of the perturbation, and it appears that the validity of this linearization is independent of the Reynolds number of the primary rotation. Attention is then restricted to the case in which the Reynolds number is large, the principal object of the note being to exemplify some of the properties of rotating systems at large Reynolds numbers in terms of a particularly simple mathematical model.

It is found that the cylindrical surface that touches the inner sphere (the axis being the axis of rotation) is a singular surface in which velocity gradients are very large. Everywhere outside this cylinder, the fluid rotates as a rigid body with the same angular velocity as the outer sphere. Inside the cylinder, the velocity distribution in the central (inviscid) core of the motion is shown to be determined by the velocity distribution in the boundary layers over the spheres, and explicit solutions are obtained for all these velocity distributions. The mechanics of the cylindrical shear layer itself is also discussed, though no explicit solution is obtained in this case.

The speed of free floating bodies on the surface of a water stream in a sloping channel has been found to be sensibly the same as the mean speed of the layer of water in which the bodies are floating, contrary to some recorded opinions.

In this paper the spatial variations and spectral structure of steady-state turbulent shear flow in channels are investigated without the introduction of empirical parameters. This is made possible by the assumption that the non-linear momentum transport has only stabilizing effects on the mean field of flow. Two constraints on the possible momentum transport are drawn from this assumption: first, that the mean flow will be statistically stable if an Orr-Sommerfeld type equation is satisfied by fluctuations of the mean; second, that the smallest scale of motion that can be present in the spectrum of the momentum transport is the scale of the marginally stable fluctuations of the mean. Within these two constraints, and for a given mass transport, an upper limit is sought for the rate of dissipation of potential energy into heat. Solutions of the stability equation depend upon the shape of the mean velocity profile. In turn, the mean velocity profile depends upon the spatial spectrum of the momentum transport. A variational technique is used to determine that momentum transport spectrum which is both marginally stable and produces a maximum dissipation rate. The resulting spectrum determines the velocity profile and its dependence on the boundary conditions. Past experimental work has disclosed laminar, ‘transitional’, logarithmic and parabolic regions of the velocity profile. Several experimental laws and their accompanying constants relate the extent of these regions to the boundary conditions. The theoretical profile contains each feature and law that is observed. First approximations to the constants are found, and give, in particular, a value for the logarithmic slope (von Kármán's constant) which is within the experimental error. However, the theoretical boundary constant is smaller than the observed value. Turbulent channel flow seems to achieve the extreme state found here, but a more decisive quantitative comparison of theory and experiment requires improvement in the solutions of the classical laminar stability problem.

Small spheroidal particles suspended in a sheared viscous liquid are sometimes observed to take up slowly preferred orientations, relative to the motion of the undisturbed liquid, which are independent of the initial conditions of release. These obsevations cannot be accounted for by the solution, obtained by Jeffery (1922), of the linearized Navier-Stokes equations. It is shown in this paper that the effect of the inertia of the liquid is to alter slowly the orbit of the particle in accordance with Jeffery's hypothesis that the particle ultimately moves in such a way that the dissipation of energy is a minimum, but that this effect is orders of magnitude too small to account for any of the experimental observations.

It is suggested that non-Newtonian properties of the liquid account for the observations. It is shown that the rate of orientation of a particle would then be independent of its size, and this prediction is verified experimentally. Other experimental evidence in support of this suggestion is also described.

Some remarks are also made about the possible effect of collisions between the particles when more than one particle is present.