Coupling between internal waves and shear-induced turbulence in stellar radiation zones: the critical layers

¹ Laboratoire AIM, CEA/DSM – CNRS – Université Paris Diderot, IRFU/SAp Centre de Saclay, 91191 Gif-sur-Yvette, France
e-mail: lucie.alvan@cea.fr; stephane.mathis@cea.fr
² Geneva Observatory, University of Geneva, chemin des Maillettes 51, 1290 Sauverny, Switzerland
e-mail: thibaut.decressin@unige.ch

Received: 31 January 2013
Accepted: 5 March 2013

Abstract

Context. Internal gravity waves (IGW) are known as one of the candidates for explaining the angular velocity profile in the Sun and in solar-type main-sequence and evolved stars due to their role in the transport of angular momentum. Our contribution deals with critical layers, which are defined as the locations where the Doppler-shifted frequency of the wave approaches zero (i.e., they correspond to corotation resonances).

Aims. The IGW propagate through stably stratified radiative regions, where they extract or deposit angular momentum through two processes: radiative and viscous dampings and critical layers. Our goal is to obtain a complete picture of the effects of these processes.

Methods. First, we expose a mathematical resolution of the equation of propagation for IGW in adiabatic and non-adiabatic cases near critical layers. Then, the use of a dynamical stellar evolution code, which treats the secular transport of angular momentum, allows us to apply these results to the case of a solar-like star.

Results. The analysis reveals two cases depending on the value of the Richardson number at critical layers: a stable one, where IGW are attenuated as they pass through a critical level, and an unstable turbulent case, where they can be reflected/transmitted by the critical level with a coefficient larger than one. Such over-reflection/transmission can have strong implications on our vision of angular momentum transport in stellar interiors.

Conclusions. This paper highlights the existence of two regimes defining the interaction between an IGW and a critical layer. An application exposes the effect of the first regime, showing a strengthening of the damping of the wave. Moreover, this work opens up new ways concerning the coupling between IGW and shear instabilities in stellar interiors.