  We study the interaction between tides and convection in astrophysical bodies
by analysing the effect of a homogeneous oscillatory shear on a fluid flow.
This model can be taken to represent the interaction between a large-scale
periodic tidal deformation and a smaller-scale convective motion. We first
consider analytically the limit in which the shear is of low amplitude and the
oscillation period is short compared to the timescales of the unperturbed flow.
In this limit there is a viscoelastic response and we obtain expressions for
the effective elastic modulus and viscosity coefficient. The effective
viscosity is inversely proportional to the square of the oscillation frequency,
with a coefficient that can be positive, negative or zero depending on the
properties of the unperturbed flow. We also carry out direct numerical
simulations of Boussinesq convection in an oscillatory shearing box and measure
the time-dependent Reynolds stress. The results indicate that the effective
viscosity of turbulent convection falls rapidly as the oscillation frequency is
increased, attaining small negative values in the cases we have examined,
although significant uncertainties remain because of the turbulent noise. We
discuss the implications of this analysis for astrophysical tides.
