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

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.