Large Scale Convection in Stars : Towards a Model for the Action of Coherent Structures Michel Rieutord 1>2 and Jean-Paul Zahn J 1 Observatoire Midi Pyrenees, 14 av. E. Belin, 31400 Toulouse, Prance 2 CERFACS, 42 av. Coriolis, 31057 Toulouse, France Abstract: We show that, representing the descending fluid in a convection zone by a porous medium, the differential rotation of the (rising) fluid is very close to that in an axisymmetric model of the convection zone with anisotropic viscosity. 1. Introduction The computation of large scale convective flows in astrophysical objects is certainly one of the great challenge of contemporary astrophysics. The computation of such flows is a basic requirement for understanding the dynamical behaviour of stars or planets. The huge Reynolds number of the flow, due to the large size of the objects, makes the flow highly turbulent and so very difficult to compute. The main problem is that we do not have, for the moment, a complete theory of turbulence. Until now two approaches have been considered: firstly the mean field approach and secondly direct numerical simulations. These two approaches possesses some major drawbacks which need to be recapitulated. The mean field approach (see Rudiger, 1989 and references therein) is con- cerned, in the case of stars, with the determination of the long term evolution of the mean axisymmetric fields. Indeed, we wish to know the nature of the mecha- nism that maintains the differential rotation or governs the magnetic activity. The mean is thus defined as to smooth out longitudinal and short-time dependence of the phenomena. For instance, if we are interested in the velocity field, we set : u = U + u', (1) where u' stands for the fluctuation around the mean U — (u). The evolution of the mean U can be derived, and, in the case of an incompressible fluid, gives the Reynolds equation d t Ui + UjVjUi = -ViP + vAUi - djR ih (2) , available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0252921100079367 Downloaded from https://www.cambridge.org/core. IP address: 181.215.83.72, on 25 Apr 2020 at 00:05:14, subject to the Cambridge Core terms of use