An experimental study has been made of the hydrodynamic stability of viscous flow between coaxial rotating cylinders with a superposed radial thermal gradient. For the data presented, the outer cylinder is at rest and the annulus is small. The axis of the cylinders is vertical; the fluid is water. There is a qualitative difference between the type of instability which first sets in when the thermal gradient is zero or nonzero: the secondary motion when the gradient is nonzero does not consist of toroidal Taylor cells. However, there is a transition to Taylor cells at a higher Taylor number. Free convection affects the results strongly. Quantitative data concerning the transition to Taylor cells are presented along with a qualitative description of the cells which first cause instability.

Measurements have been made of the wavelength of Taylor vortices between rotating cylinders. It is shown that the relaxation time of such a vortex system is approximatelyL2/6v, whereLis the length of the vortex column andvis the kinematic viscosity. Previous measurements reported in the literature have not been steady-state measurements because of the long relaxation time. The present data are accurate to 1% and extend to 40 times the critical Taylor number. The variation of wavelength with Taylor number is linear and the slope is exceedingly small and negative. The non-uniqueness of wave-number observed by Coles (1965) in doubly periodic flows is here shown to occur in the rotationally symmetric case. It is argued that variational methods are inapplicable in determining the wave-number of finite-amplitude secondary flows. The experimental results show that the wave-number is determined uniquely by the initial conditions of the system. It is suggested that any method which neglects the time-dependent behaviour of the system cannot select the final state from the manifold of solutions which occur in non-linear problems.

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Measurements have been made of the onset of instability in rotating Couette flow in order to check some recent numerical results. The case of a very wide gap, a medium gap, and a very narrow clearance ratio have been studied. The accuracy of the results is about ± 2%. The present data and other values available in the literature are compared with the computations of different investigators. With a few exceptions the agreement is found to be excellent. End effects are described and their relative importance is discussed. Methods of scaling the results are evaluated. A simple formula is presented for calculating the onset value when only the inner cylinder rotates.