Three-dimensional stability of the solar tachocline

¹ Astrophysikalisches Institut Potsdam, An der Sternwarte 16, Germany e-mail: rarlt@aip.de
² Isaac Newton Institute for Mathematical Sciences, 20 Clarkson Road, Cambridge CB3 0EH, UK

Received: 24 February 2005
Accepted: 20 May 2005

Abstract

The three-dimensional, hydrodynamic stability of the solar tachocline was investigated based on a rotation profile as a function of both latitude and radius. By varying the amplitude of the latitudinal differential rotation, we found linear stability limits at various Reynolds numbers by numerical computations. We repeated the computations with different latitudinal and radial dependences of the angular velocity. The stability limits are all higher than those previously found from two-dimensional approximations and higher than the shear expected in the Sun. It is concluded that any part of the tachocline which is radiative is hydrodynamically stable against small perturbations.