  In close exoplanetary systems, tidal interactions drive orbital and spin
evolution of planets and stars over long timescales. Tidally-forced inertial
waves (restored by the Coriolis acceleration) in the convective envelopes of
low-mass stars and giant gaseous planets contribute greatly to the tidal
dissipation when they are excited and subsequently damped (e.g. through 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 study, we use a realistic tidal body forcing
to excite inertial waves through the residual action of the equilibrium tide in
the momentum equation for the waves. By performing 3D nonlinear hydrodynamical
simulations in adiabatic and incompressible convective shells, we investigate
how the addition of nonlinear terms affects the tidal flow properties, and the
energy and angular momentum redistribution. In particular, we identify and
justify the removal of terms responsible for unphysical angular momentum
evolution observed in a previous numerical study. 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. We also highlight the major role of both
corotation resonances and parametric instabilities of inertial waves, which are
observed for sufficiently high tidal forcing amplitudes or low viscosities, in
affecting the tidal flow response.

Solar and Stellar Astrophysics;Earth and Planetary Astrophysics;Fluid Dynamics