  Tidal dissipation in star-planet systems can occur through various
mechanisms, among which is the elliptical instability. This acts on
elliptically deformed equilibrium tidal flows in rotating fluid planets and
stars, and excites inertial waves in convective regions if the dimensionless
tidal amplitude ($\epsilon$) is sufficiently large. We study its interaction
with turbulent convection, and attempt to constrain the contributions of both
elliptical instability and convection to tidal dissipation. For this, we
perform an extensive suite of Cartesian hydrodynamical simulations of rotating
Rayleigh-B\'{e}nard convection in a small patch of a planet. We find that tidal
dissipation resulting from the elliptical instability, when it operates, is
consistent with $\epsilon^3$, as in prior simulations without convection.
Convective motions also act as an effective viscosity on large-scale tidal
flows, resulting in continuous tidal dissipation (scaling as $\epsilon^2$). We
derive scaling laws for the effective viscosity using (rotating) mixing-length
theory, and find that they predict the turbulent quantities found in our
simulations very well. In addition, we examine the reduction of the effective
viscosity for fast tides, which we observe to scale with tidal frequency
($\omega$) as $\omega^{-2}$. We evaluate our scaling laws using interior models
of Hot Jupiters computed with MESA. We conclude that rotation reduces
convective length scales, velocities and effective viscosities (though not in
the fast tides regime). We estimate that elliptical instability is efficient
for the shortest-period Hot Jupiters, and that effective viscosity of turbulent
convection is negligible in giant planets compared with inertial waves.

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