ON THE OVERSTABILITY CONVECTION

Abstract

The oscillatory mode of instability in a rotating fluid layer heated from below is theoret-ically investigated with a combination of Eulerian and Lagrangian analyses. An exact analysisis not only nmde for the case of two free bounding surfaces, but for the case of one free andone rigid bounding surfaces. The physics of overstability convection is attributable to the dual role of the thermaldiffusion in this rotating fluid Thermal diffusion ordinarily only destroys the buoyancy offluid parcels. But if the rotation rate is sufficiently large and if the viscous dissipation iscomparatively weak, the heat exchanges alternately produce overcooling and overheating of theparcels and thereby give rise to a net positive feedback mechanism for the instability. The parcels near a rigid bounding surface (they are different from those near a freebounding surface), however, do not have a net horizontal drift and penetrate more and moreinto the interior of the layer, and they just progressively drift towards the rigid surface. Andthe vertical velocity near the rigid surface layer lags behind that in the bulk of the interiorlayer by a quarter of the oscillation period. These differences stem from the dynamical effectsof the frictionally induced secondary circulation known as Ekman pumping and suction. The spatially averaged energetics of oscillatory unstable modes are examined and discussed. On the basis of the theoretical results, it is suggested that the observod oscillatory vortexin a laboratory simulation of the flow over a heated Qinghai-Xizang model plateau (Researchon Experimental Simulation, 1978) may be interpreted in terms of the notion of overstabilityconvection.