Non linear waves in two dimensional keplerian flows

Abstract

Accretion discs in astrophysics are fundamental for converting gravitational binding energy into observed electromagnetic radiation. We study the behavior of waves in a two dimensional supersonic Keplerian flow inside a given gravitational potential. We present the effects of shearing and rotation on short waves, and the numerical study of the dynamical stability of such flows with respect to various perturbations. We show that a large class of dynamical effects, due to pressure and associated to short time scales, may be excited.     

Derivation of the amplitude equations of acoustic modes of an unstable semi-infinite polytrope

The coupling of non-radial pulsations and convection is studied on a simple example: an unstable semi-infinite polytrope. An expansion is proposed and the equations that should describe correctly the pulsations are isolated. The additional complications of the real solar case are discussed at the end.