On the spatial oscillations of a horizontally heated rotating fluid

A laboratory model simulating aspects of oceanic or atmospheric circulation consists of a rotating fluid annulus which is subject to a temperature gradient on the lower surface and is insulated on the inner and outer curved walls and on the top surface. A theoretical study of the resulting steady axisymmetric fluid motion in the limit of small Ekman number, E, by Daniels (1976) indicated that if an appropriate convective parameter is sufficiently large, oscillatory solutions are generated in the E to the 1/3-power layer which is located on the hotter of the two side-walls, which do not decay into the geostrophic interior. The present paper resolves this difficulty by using the method of multiple scales to trace the development of the oscillatory solutions in the interior of the fluid. This leads to a consistent overall flow pattern throughout the annulus, except at an infinite set of discrete values of the convective parameter at which resonance is predicted.