Quasigeostrophic models of convection in rotating spherical shells

Abstract

The use of a quasigeostrophic, two-dimensional approximation in the problem of convection in a rapidly rotating spherical shell has been limited so far to investigations of the qualitative behavior of the solution. In this study, we build a quasigeostrophic model that agrees quantitatively with full threedimensional solutions of the onset of convection in the case of differential heating. Reducing the dimensionality of the problem also permits the simulation of finite amplitude regimes of convection, up to quasigeostrophic turbulence. The nonlinear behavior of the system is studied in detail and compared to ultrasonic Doppler velocimetry measurements performed in a convecting, rapidly rotating spherical shell filled with water and liquid gallium. The results are quantitatively satisfactory and open the way to less computer-demanding, and still accurate, simulations of the geodynamo. © 2003 by the American Geophysical Union.