Flow through a rapidly rotating conduit of arbitrary cross-section

The problem of flow through rotating channels of almost arbitrary cross-section is considered. It is shown that when the ratio of the Rossby number and the Reynolds number is small (ε = Ro/Re [Lt ] 1) and when the Reynolds number is not too large (Re [Lt ] ε−1): (1) the viscous effects are important only in thin boundary layers along the channel walls; (2) the flow in the interior is geostrophic; and (3) the inertia effects may be neglected everywhere. Solutions for the geostrophic region and the boundary layers are obtained and are combined to give the complete velocity field. Experimental results for a circular conduit are presented which are in good agreement with the theory.