Nonlinear tidal interactions in the convective envelopes of low-mass stars and giant gaseous planets

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 magnetised convective envelope, as is also expected in giant gaseous planets like Hot-Jupiter. Tidal flows, and more specifically inertial waves (restored by the Coriolis acceleration, and recently discovered in the Sun) tidally-excited, are the main direct manifestation of tidal interactions in the convective envelopes of these bodies. Furthermore, inertial waves are small-scale waves that are sensitive to nonlinearities, especially in close Hot-Jupiter systems with strong tidal forcing. The nonlinear self-interaction of inertial waves is known to trigger differential rotation in convective shells, as shown in numerical and experimental hydrodynamical studies. Since inertial waves are a key contribution to the tidal dissipation in close star-planet systems, it is essential to have the finest understanding of tidal inertial wave propagation and dissipation in such a complex nonlinear, magnetised, and differentially rotating environment.
In this context, we investigate how nonlinearities affect the tidal flow properties, thanks to new 3D hydrodynamic and magneto-hydrodynamic nonlinear simulations of tides, in an adiabatic and incompressible convective shell. First, we show to what extent the emergence of differential rotation is modifying the tidal dissipation rates, prior to linear predictions. In this newly generated zonal flows, nonlinear self-interactions of tidal inertial waves can also trigger different kind of instabilities and resonances between the waves and the background sheared flow, when the tidal forcing is strong enough or the viscosity low enough. These different processes disrupt the energetic exchanges between tidal waves and the background flow, and also further modifies the tidal dissipation rates. Secondly, we present the first non-linear numerical analysis of tidal flows in a magnetised convective shell. One main effect of the magnetic field in our model is to mitigate zonal flows triggered by the nonlinear interaction of inertial waves. The consequences for tidal flows are important, since the installation of zonal flows in nonlinear hydrodynamical simulations is the main cause of significant changes in tidal dissipation and angular momentum exchanges, compared to linear predictions for a uniformly rotating body.