Supercritical convection associated with ultrafast MHD rotation

Abstract

Highly nonlinear buoyant convection is investigated analytically under conditions typically encountered in the liquid cores of planets in the solar system. As a result of the supercritical behavior (enormous Rayleigh number) and ultrafast rotation (small Ekman number) typical of such flows, diffusion and viscosity act only in layers that are asymptotically thin in comparison with the radius of the core. These boundary layers control the buoyancy, the large-scale velocity, and the magnetic field observed at the planetary surface. The interchange of the internal layers determines the small-scale (unobservable) fields and the prevailing symmetry of the large-scale magnetic fields. It is proved for the first time that axisymmetric azimuthal flows dominate at large scales, while convection cells elongated parallel to the axis of rotation dominate at small scales. A system of equations is derived which is optimum for describing magnetoconvection of planetary cores on both large and small scales. It yields estimates in superb agreement with expensive numerical and experimental models of supercritical convection associated with rapid rotation. Such models will be capable of solving the MHD dynamo problem only when their algorithms are made consistent with the asymptotic limits presented here.