Thermal Convection in a Rotating Fluid Annulus: Part 3. Suppression of the Frictional Constraint on Lateral Boundaries

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Abstract
In certain rotating fluid systems such as the atmosphere, the flow must maintain a zero net torque on the horizontal surface. The character of such flows is sought through numerical integration of the Navier-Stokes equations. The fluid occupies a torus shaped region whose vertical boundaries are assumed to be frictionless. The solutions relate to either a laboratory annulus with hypothetical free-slip sidewalls or to a zonal strip of the atmosphere or ocean. All the solutions are qualitatively similar despite parametric differences; their flows have a westerly-easterly zonal wind distribution near the horizontal boundary together with direct and indirect cells in a manner reminiscent of that proposed by classical theory for the general circulation of the atmosphere. Under a strong external temperature differential the isotherms concentrate into a front. The meridional circulation assumes the form of gliding motion parallel to the front together with frictionally driven secondary circulations. Certain mesoscale geophysical phenomena also possess these characteristics. The solutions provide good examples of Eliassen's theory of vortex circulations.

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