The effect of sloping boundaries on baroclinic instability in two related internally heated, rotating fluid systems

Results have been obtained from two internally heated, rotating fluid syste ms with differing aspect ratios, in which a beta-effect (variation in Corio lis parameter with latitude) has been simulated by the inclusion of opposit ely sloping endwalls. The boundaries are arranged so that the fluid depth ( D) can either increase with radius (partial derivative D/partial derivative r > 0) or decrease with radius (partial derivative D/partial derivative r < 0). In both systems, stable eddy features are observed over a wide range of rotation rates for each endwall arrangement. While a large number of dif ferent azimuthal wavenumber (m) modes are seen in the regular wave regime o f the partial derivative D/partial derivative r > 0 endwall experiments, on ly the gravest mode (m = 1) is seen in the regular wave regime of the parti al derivative D/partial derivative r < 0 endwall experiments. Within the fo rmer experimental arrangement, the radial scale of the eddy features is sho wn to be approximately that of the Rhines scale L-beta = pi root 2U/beta, w hile in the partial derivative D/partial derivative r < 0 endwall experimen ts the eddy kinetic energy is seen to penetrate the L-beta scale and accumu late at the largest domain-filling scales. This remarkable difference in th e flow structure of the two endwall arrangements may find a partial explana tion in terms of established results on the instability of finite amplitude barotropic Rossby waves, where partial derivative D/partial derivative r < 0 endwalls remove the stability thresholds on wave amplitudes for all but the gravest mode. (C) 1999 Elsevier Science Ltd. All rights reserved.