STELLAR EVOLUTION WITH ROTATION - III - MERIDIONAL CIRCULATION WITH MU-GRADIENTS AND NON-STATIONARITY

Models of stellar evolution with rotation are very much needed in orde r to interpret recent stellar properties, in particular for massive st ars. For that we proceed to a detailed investigation of some critical physical processes in rotating stars: 1. The equation expressing the t ransport of angular momentum by circulation and diffusion is revised t o also account for expansion and contraction in non-stationary models. 2. We examine the current expressions for the velocity U(tau) of the meridional circulation, also taking into account mu-gradients and hori zontal turbulence. We show that there are no ''mu-currents'' but just meridional currents which can be sizeably influenced by the gradients of mean molecular weight mu. A proper account of the mu-gradients may reduce U(tau) by one or two orders of magnitude with respect to curren t expressions. 3. While the usual expressions for the meridional circu lation would predict an infinite velocity at the edge of a radiative a nd semiconvective zone and an inverted circulation in a semiconvective zone, the present developments give a continuity of the solutions for the circulation. 4. The approximation of a stationary circulation, wh ich is no longer valid after the main-sequence phase, is also removed and the case of a general equation of state is considered. We notice t hat in the stationary regime the horizontal fluctuations of mu represe nt some fixed fraction of the vertical mu-gradient. To first order, th is fraction is not dependent on rotation, because the building of hori zontal fluctuations by the circulation is compensated by the smoothing due to horizontal turbulence.