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Turbulent convection is thought to act as an effective viscosity in dampingequilibrium tidal flows, driving spin and orbital evolution in close convectivebinary systems. Compared to mixing-length predictions, this viscosity ought tobe reduced when the tidal frequency $|\omega_t|$ exceeds the turnover frequency$\omega_{c\nu}$ of the dominant convective eddies, but the efficiency of thisreduction has been disputed. We reexamine this long-standing controversy usingdirect numerical simulations of an idealized global model. We simulate thermalconvection in a full sphere, and externally forced by the equilibrium tidalflow, to measure the effective viscosity $\nu_E$ acting on the tidal flow when$|\omega_t|/\omega_{c\nu} \gtrsim 1$. We demonstrate that the frequencyreduction of $\nu_E$ is correlated with the frequency spectrum of the(unperturbed) convection. For intermediate frequencies below those in theturbulent cascade ($|\omega_t|/\omega_{c\nu} \sim 1-5$), the frequency spectrumdisplays an anomalous $1/\omega^\alpha$ power law that is responsible for thefrequency-reduction $\nu_E \propto 1/|\omega_t|^{\alpha}$, where $\alpha < 1$depends on the model parameters. We then get $|\nu_E| \propto1/|\omega_t|^{\delta}$ with $\delta > 1$ for higher frequencies, and $\delta=2$is obtained for a Kolmogorov turbulent cascade. A generic $|\nu_E| \propto1/|\omega_t|^{2}$ suppression is next found for higher frequencies within thedissipation range of the convection (but with negative values). Our resultsindicate that a better knowledge of the frequency spectrum of convection isnecessary to accurately predict the efficiency of tidal dissipation in starsand planets resulting from this mechanism.

Efficiency of tidal dissipation in slowly rotating fully convective stars or planets