Interactions of tidal and precessional flows with convection: applications to tidal dissipation in giant planets and stars

Gravitational tidal interactions between two astrophysical bodies can result in evolution of their spins and orbits. These interactions are caused by dissipation of tidal energy and associated transfer of angular momentum. Of particular interest are the close-in giant exoplanets known as Hot Jupiters, because strong tidal dissipation is expected in their own fluid envelopes as well as their host stars. In the study of tides, the fluid response is often split into an equilibrium tide and a dynamical tide. We will focus on three dissipation mechanisms of the equilibrium tide in convection zones of Hot Jupiters. The first is the action of turbulent convection in damping tidal flows, while the other two are the elliptical and precessional instabilities. Both of these instabilities are parametric in nature and excite inertial waves. The elliptical instability is excited because of the tidal deformation of the body due to the equilibrium tide, while axial precession and the associated precessional flow allows for the precessional instability. To study these mechanisms we analyse a large number of Boussinesq local Cartesian box simulations covering a wide range of parameters. We have found that the elliptical instability and rotating convection both generate large-scale vortices in the flow, which inhibit the elliptical instability at small tidal amplitudes or strong convective driving. The tidal dissipation due to the precessional instability on the other hand is reduced instead of being inhibited by convection. We find that convective turbulence acts on both flows like an effective viscosity resulting in continuous tidal dissipation. This effective viscosity can be described well using rotating mixing-length theory. Furthermore, we find the effective viscosity to be strongly reduced in the fast tides regime, where the tidal frequency exceeds the convective one, in these rotating simulations. Finally, we have generated interior models of giant planets, and find that Jupiter and Hot Jupiters are firmly in the fast tides regime. We estimate that both the elliptical and precessional instabilities are efficient for the shortest period Hot Jupiters, and that the effective viscosity of turbulent convection is likely to be negligible in giant planets compared with inertial wave mechanisms.