The coupling between internal waves and shear-induced turbulence in stellar radiation zones: the critical layer

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.Comment: 17 pages, 8 figure

Theoretical seismology in 3D : nonlinear simulations of internal gravity waves in solar-like stars

Internal gravity waves (hereafter IGWs) are studied for their impact on the angular momentum transport in stellar radiation zones and the information they provide about the structure and dynamics of deep stellar interiors. We here present the first 3D nonlinear numerical simulations of IGWs excitation and propagation in a solar-like star. The aim is to study the behavior of waves in a realistic 3D nonlinear time dependent model of the Sun and to characterize their properties. We compare our results with theoretical and 1D predictions. It allows us to point out the complementarity between theory and simulation and to highlight the convenience but also the limits of the asymptotic and linear theories. We show that a rich spectrum of IGWs is excited by the convection, representing about 0.4% of the total solar luminosity. We study the spatial and temporal properties of this spectrum, the effect of thermal damping and nonlinear interactions between waves. We give quantitative results about the modes frequencies, evolution with time and rotational splitting and we discuss the amplitude of IGWs considering different regimes of parameters. This work points out the importance of high performance simulation for its complementarity with observation and theory. It opens a large field of investigation concerning IGWs propagating nonlinearly in 3D spherical structures. The extension of this work to other types of stars, with different masses, structures and rotation rates will lead to a deeper and more accurate comprehension of IGWs in stars.Comment: 27 pages, 29 figures, accepted for publication in A&A (13/03/2014

Corotation resonances for gravity waves and their impact on angular momentum transport in stellar interiors

Gravity waves, which propagate in radiation zones, can extract or deposit angular momentum by radiative and viscous damping. Another process, poorly explored in stellar physics, concerns their direct interaction with the differential rotation and the related turbulence. In this work, we thus study their corotation resonances, also called critical layers, that occur where the Doppler-shifted frequency of the wave approaches zero. First, we study the adiabatic and non-adiabatic propagation of gravity waves near critical layers. Next, we derive the induced transport of angular momentum. Finally, we use the dynamical stellar evolution code STAREVOL to apply the results to the case of a solar-like star. The results depend on the value of the Richardson number at the critical layer. In the first stable case, the wave is damped. In the other unstable and turbulent case, the wave can be reflected and transmitted by the critical layer with a coefficient larger than one: the critical layer acts as a secondary source of excitation for gravity waves. These new results can have a strong impact on our understanding of angular momentum transport processes in stellar interiors along stellar evolution where strong gradients of angular velocity can develo

Impact of general differential rotation on gravity waves in rapidly rotating stars

4 pages, 5 figures, to appear in the proceedings of the PHOST conference in honour of Pr. ShibahashiInternational audienceDifferential rotation plays a key role in stellar evolution by triggering hydrodynamical instabilities and large-scale motions that induce transport of chemicals and angular momentum and by modifying the propagation and the frequency spectrum of gravito-inertial waves. It is thus crucial to investigate its effect on the propagation of gravity waves to build reliable seismic diagnostic tools, especially for fast rotating stars, where perturbative treatments of rotation fail. Generalising a previous work done in the case of uniform rotation, we derived a local dispersion relation for gravity waves in a differentially rotating star, taking the full effect of rotation (both Coriolis and centrifugal accelerations) into account. Then we modelled the propagation of axisymmetric waves as the propagation of rays. This allowed us to efficiently probe the properties of the waves in various regimes of differential rotation