Abstract

In close exoplanetary systems, tidal interactions are known to shape the orbital architecture of the system, modify star and planet spins, and have an impact on the internal structure of the bodies through tidal heating. Most stars around which planets have been discovered are low-mass stars and thus feature a convective envelope, as is also expected in giant gaseous planets like Hot-Jupiter. The dissipation of tidal flows, and more specifically the dissipation of tidal inertial waves (restored by the Coriolis acceleration) can be particularly important in the convective envelopes, especially in the early stage of the life of the system. In parallel, the nonlinear self-interaction of inertial waves is known to affect the structure of the background flow by triggering differential rotation in convective shells, as shown in numerical and experimental hydrodynamical studies.

In this context, I will review and show how the addition of nonlinearities affects the tidal flow properties, the energy and angular momentum balances, thanks to 3D hydrodynamic nonlinear simulations of tides, in an adiabatic and incompressible convective shell. Using a realistic forcingto tidally excite inertial waves, we show that cylindrical differential rotation still develops in our model due to the non uniform deposition of angular momentum, when shear layers (straight structures where the waves are focused) are activated inside the shell. Moreover we do not observe unexpected angular momentum evolution leading to the desynchronisation of the bodies, as reported in some previous simulations. I willexplain to what extent and how the emergence of differential rotation is modifying the tidal dissipation rates, prior to linear predictions. Furthermore, nonlinear self-interactions of tidal inertial waves in the newly generated zonal flows can also trigger different kind of instabilities and resonances, when the tidal forcing is strong enough or the viscosity low enough. These various interactions between tidal inertial waves and sheared zonal flows reshape the energetic exchanges inside the shell, and also further modifies tidal dissipation rates.