  Tidal interactions are important in driving spin and orbital evolution in
planetary and stellar binary systems, but the fluid dynamical mechanisms
responsible remain incompletely understood. One key mechanism is the
interaction between tidal flows and convection. Turbulent convection is thought
to act as an effective viscosity in damping large-scale tidal flows, but there
is a long-standing controversy over the efficiency of this mechanism when the
tidal frequency exceeds the turnover frequency of the dominant convective
eddies. This high frequency regime is relevant for many applications, such as
for tides in stars hosting hot Jupiters. We explore the interaction between
tidal flows and convection using hydrodynamical simulations within a local
Cartesian model of a small patch of a convection zone of a star or planet. We
adopt the Boussinesq approximation and simulate Rayleigh-B\'enard convection,
modelling the tidal flow as a background oscillatory shear flow. We demonstrate
that the effective viscosity of both laminar and turbulent convection is
approximately frequency-independent for low frequencies. When the forcing
frequency exceeds the dominant convective frequency, the effective viscosity
scales inversely with the square of the tidal frequency. We also show that
negative effective viscosities are possible, particularly for high frequency
tidal forcing, suggesting the surprising possibility of tidal anti-dissipation.
These results are supported by a complementary high frequency asymptotic
analysis that extends prior work by Ogilvie & Lesur. We discuss the
implications of these results for interpreting the orbital decay of hot
Jupiters, and for several other astrophysical problems.
