TURBULENT TRANSPORT IN STELLAR INTERIORS

Differential rotation is probably the major cause of turbulence in sta bly stratified stellar interiors. The boundary of the superficial sola r convection zone plays a critical role for both the large scale circu lation and the differential rotation. The turbulence arises from the b arotropic instability in a vertically stratified medium and is expecte d to be anisotropic. It tends to suppress one of its causes, namely di fferential rotation in latitude. It offers an explanation for the thin ness of the solar tachocline, the boundary layer beneath the convectio n zone where solar seismology shows that rotation varies from differen tial above to apparently uniform below. The anisotropy of turbulence a lso strongly reduces the efficiency of vertical particle transport. We show that for an anisotropy A of horizontal to vertical velocities, t he vertical diffusivity is a factor AZ less than the horizontal diffus ivity. Transport by meridional circulation is also reduced, as well as the efficiency of a composition gradient in suppressing meridional ci rculation. These effects of anisotropy explain the very small upper li mit that observations of the concentration of chemical elements impose to vertical transport in stars. However the recent results of heliose ismology, that the solar core rotates at nearly the same rate as the w hole radiative zone, cannot currently be explained by anisotropic turb ulent transport. It suggests the need for an additional transport proc ess such as a magnetic torquing or gravity waves. Furthermore, near th e base of the convection zone, magnetic instabilities could provide an alternate mechanism to mix angular momentum preferentially in latitud e 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 accurac y. This should allow us to distinguish between the various hydrodynami cal and hydromagnetic models.