Axisymmetric flow and stability in the lower symmetry regime of a differentially heated rotating annulus of fluid

A study is made of the axisymmetric steady state which occurs in the rotating annulus when the thermal Rossby number is small. An approximate solution of the governing equations for the axisymmetric state is obtained by the methods of singular perturbation theory. The higher order effects of centrifugal forces and convection in the side wall boundary layers in determining the structure of the velocity and temperature fields in the interior of the fluid is discussed. An analysis is made of the stability of the axisymmetric state also using the methods of singular perturbation theory. The first part of this analysis is concerned with the stability of wave-like disturbances with low wave numbers. It is shown that these will be stable if the thermal Rossby number is finite and sufficiently small.