  Internal gravity waves (hereafter IGWs) 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 bringing concerns critical layers, a process poorly explored in
stellar physics, defined as the location where the local relative frequency of
a given wave to the rotational frequency of the fluid tends to zero (i.e that
corresponds to co-rotation resonances). 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 this latters. First, we expose a
mathematical resolution of the equation of propagation for IGWs 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.The analysis
reveals two cases depending on the value of the Richardson number at critical
layers: a stable one, where IGWs 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. 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 new ways
concerning the coupling between IGWs and shear instabilities in stellar
interiors.
