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Convection is thought to act as a turbulent viscosity in damping tidal flowsand in driving spin and orbital evolution in close convective binary systems.This turbulent viscosity should be reduced, compared to mixing-lengthpredictions, when the forcing (tidal) frequency $|{\omega}_t|$ exceeds theturnover frequency ${\omega}_{cv}$ of the dominant convective eddies. However,two contradictory scaling laws have been proposed and this issue remains highlydisputed. To revisit this controversy, we conduct the first direct numericalsimulations (DNS) of convection interacting with the equilibrium tidal flow inan idealized global model of a low-mass star. We present direct computations ofthe turbulent effective viscosity, ${\nu}_E$, acting on the equilibrium tidalflow. We unexpectedly report the coexistence of the two disputed scaling laws,which reconciles previous theoretical (and numerical) findings. We recover theuniversal quadratic scaling ${\nu}_E \propto (|{\omega}_t|/{\omega}_{cv})^{-2}$in the high-frequency regime $|{\omega}_t|/{\omega}_{cv} \gg 1$. Our resultsalso support the linear scaling ${\nu}_E \propto(|{\omega}_t|/{\omega}_{cv})^{-1}$ in an intermediate regime with $1 \leq|{\omega}_t|/{\omega}_{cv} = \mathcal{O}(10)$. Both regimes may be relevant toexplain the observed properties of close binaries, including spinsynchronization of solar-type stars and the circularization of low-mass stars.The robustness of these two regimes of tidal dissipation, and the transitionbetween them, should be explored further in more realistic models. A betterunderstanding of the interaction between convection and tidal flows is indeedessential to correctly interpret observations of close binary stars andshort-period planetary orbits.

Turbulent viscosity acting on the equilibrium tidal flow in convective stars