Tidal flow modelling in convective shells of stars and planets

Tidal interactions play a crucial role in driving spin-orbit evolution in close stellar and planetary systems. The dissipation of energy carried by tidally-driven flows in the fluid envelopes of stars and planets is an efficient way of exchanging angular momentum in these systems. In rotating convective zones, tidally-excited inertial waves (i.e. those restored by the Coriolis acceleration) are likely to contribute the most to tidal dissipation. Moreover, when the tidal forcing is strong, namely in compact systems such as Hot Jupiter systems, the tidal flows are sensitive to non-linear effects. Although magnetism is likely to be ubiquitous in host solar-like stars and giant gaseous planets with convective region(s), most studies have treated tidal flows in linear hydrodynamic two-dimensional models.  In recent years, we have developed a numerical model to study nonlinear tidal flows in a 3D convective spherical shell using the pseudo-spectral code MagIC. We found that the nonlinear self-interaction of inertial waves can trigger differential rotation in convective shells in the form of zonal flows, which can significantly alter tidal dissipation rates from prior linear predictions with uniform rotation. Recently, we investigated the effect of an initial dipolar magnetic field on tidal waves and their feedback. We found that tidally-generated zonal flows can either be destroyed or can generate a more complex magnetic field, and we will discuss these different regimes.