Turbulent Transport in Stellar Interiors

Differential rotation is probably the major cause of turbulence in stably stratified stellar interiors. The boundary of the superficial solar convection zone plays a critical role for both the large scale circulation and the differential rotation. The turbulence arises from the barotropic instability in a vertically stratified medium and is expected to be anisotropic. It tends to suppress one of its causes, namely differential rotation in latitude. It offers an explanation for the thinness of the solar tachocline, the boundary layer beneath the convection zone where solar seismology shows that rotation varies from differential above to apparently uniform below. The anisotropy of turbulence also strongly reduces the efficiency of vertical particle transport. We show that for an anisotropy A of horizontal to vertical velocities, the vertical diffusivity is a factor A ² less than the horizontal diffusivity. Transport by meridional circulation is also reduced, as well as the efficiency of a composition gradient in suppressing meridional circulation. These effects of anisotropy explain the very small upper limit that observations of the concentration of chemical elements impose to vertical transport in stars. However the recent results of helioseismology, that the solar core rotates at nearly the same rate as the whole radiative zone, cannot currently be explained by anisotropic turbulent transport. It suggests the need for an additional transport process such as a magnetic torquing or gravity waves. Furthermore, near the base of the convection zone, magnetic instabilities could provide an alternate mechanism to mix angular momentum preferentially in latitude compared with radial mixing. The quality of the helioseismology data is improving very rapidly. It holds the promise to determine, within the next few years, the velocity field within the Sun to great accuracy. This should allow us to distinguish between the various hydrodynamical and hydromagnetic models. Received 20 May 1997 and accepted 4 January 1998