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 _ { cv } 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 _ { cv } \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 _ { cv } \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 .