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 orbital architectures, to modify star and planet spins, and to have an impact on the internal structures 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 Jupiters. Tidal flows in convective envelopes consist of large-scale equilibrium tides and inertial waves (restored by the Coriolis acceleration, and recently discovered in the Sun) excited by tides. Inertial waves contribute greatly to the tidal dissipation when they are excited and subsequently damped (through e.g. turbulent viscous friction), especially early in the life of a system. These waves are known to be subject to nonlinear effects, including triggering differential rotation in the form of zonal flows. In this context, we investigate how nonlinearities affect tidal properties, thanks to 3D nonlinear hydrodynamical simulations of tidal flows, in an adiabatic and incompressible convective shell. Unlike previous studies, we use a realistic tidal body forcing to excite inertial waves. Within our new set-up, we observe the establishment of strong cylindrically-sheared zonal flows, which modify the tidal dissipation rates from prior linear theoretical predictions. We demonstrate that the effects of this differential rotation on the waves neatly explains the discrepancies between linear and nonlinear dissipation rates in many of our simulations. Nonlinear interactions between inertial waves, and those between the waves and the background sheared flow, can lead to instabilities, for sufficiently high tidal forcing amplitudes or low viscosities. These different processes disrupt the energetic exchanges between tidal waves and the background flow, and also further modify tidal dissipation rates.