  Turbulent convection is thought to act as an effective viscosity in damping
equilibrium tidal flows, driving spin and orbital evolution in close convective
binary systems. Compared to mixing-length predictions, this viscosity ought to
be reduced when the tidal frequency $|\omega_t|$ exceeds the turnover frequency
$\omega_{c\nu}$ of the dominant convective eddies, but the efficiency of this
reduction has been disputed. We reexamine this long-standing controversy using
direct numerical simulations of an idealized global model. We simulate thermal
convection in a full sphere, and externally forced by the equilibrium tidal
flow, to measure the effective viscosity $\nu_E$ acting on the tidal flow when
$|\omega_t|/\omega_{c\nu} \gtrsim 1$. We demonstrate that the frequency
reduction of $\nu_E$ is correlated with the frequency spectrum of the
(unperturbed) convection. For intermediate frequencies below those in the
turbulent cascade ($|\omega_t|/\omega_{c\nu} \sim 1-5$), the frequency spectrum
displays an anomalous $1/\omega^\alpha$ power law that is responsible for the
frequency-reduction $\nu_E \propto 1/|\omega_t|^{\alpha}$, where $\alpha < 1$
depends on the model parameters. We then get $|\nu_E| \propto
1/|\omega_t|^{\delta}$ with $\delta > 1$ for higher frequencies, and $\delta=2$
is obtained for a Kolmogorov turbulent cascade. A generic $|\nu_E| \propto
1/|\omega_t|^{2}$ suppression is next found for higher frequencies within the
dissipation range of the convection (but with negative values). Our results
indicate that a better knowledge of the frequency spectrum of convection is
necessary to accurately predict the efficiency of tidal dissipation in stars
and planets resulting from this mechanism.
