The steady-state flow in a rotating container is examined when the container is deformed into an ellipsoidal figure which is fixed in inertial space. The analysis is carried out for a fluid of small viscosity, and to the second order in Rossby number. Results show a vortex existing along the rotation axis, this being an interior manifestation of non-linear boundary-layer effects. These effects are a direct consequence of the forced oscillation being at twice the rotational frequency. The configuration is chosen to suggest the effects of gravitational body tides on the dynamics of the core of the earth. This problem is related to the similar problem of a precessing spheroid, and an experiment is described which tests the present theory and confirms previous experimental data from precessing spheroids.

The formation of shock waves in. dense argon is studied using a numerical technique related to the molecular-dynamics approach. The kinetic and total pressures, density, temperature and mass velocity are calculated when a simulated tungsten piston is driven into the stationary gas. It is found that the pressure generated is similar to that found using binary collision assumptions, however the temperature is lower and the density much higher than under more rarefied conditions. Results are also given for the same experiments when the generating piston is composed of dense argon atoms. It is shown that the results are almost independent of the type of piston material and that the shock structure is a function of the gas interparticle force law only. The reflexion of a spherically imploding shock wave in dense argon is also examined and it is found that the shock wave reflects before reaching the centre due to high tangential stresses. Some data is also given, upon the velocity distribution and wall pressure fluctuations.

A discussion is given of the current state of knowledge of vortex streets behind circular cylinders in the Reynolds number range 50 to 160. This was prompted by Gaster's (1969) report that he could not find the transition at a Reynolds number of about 90 observed by Tritton (1959) and Berger (1964a). A further brief experiment confirming the existence of the transition is described Reasons for rejecting Gaster's interpretation are advanced. Possible (mutually alternative) explanations of the discrepant observations are suggested.