  Convection is thought to act as a turbulent viscosity in damping tidal flows
and in driving spin and orbital evolution in close convective binary systems.
This turbulent viscosity should be reduced, compared to mixing-length
predictions, when the forcing (tidal) frequency $|{\omega}_t|$ exceeds the
turnover frequency ${\omega}_{cv}$ of the dominant convective eddies. However,
two contradictory scaling laws have been proposed and this issue remains highly
disputed. To revisit this controversy, we conduct the first direct numerical
simulations (DNS) of convection interacting with the equilibrium tidal flow in
an idealized global model of a low-mass star. We present direct computations of
the turbulent effective viscosity, ${\nu}_E$, acting on the equilibrium tidal
flow. We unexpectedly report the coexistence of the two disputed scaling laws,
which reconciles previous theoretical (and numerical) findings. We recover the
universal quadratic scaling ${\nu}_E \propto (|{\omega}_t|/{\omega}_{cv})^{-2}$
in the high-frequency regime $|{\omega}_t|/{\omega}_{cv} \gg 1$. Our results
also 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 to
explain the observed properties of close binaries, including spin
synchronization of solar-type stars and the circularization of low-mass stars.
The robustness of these two regimes of tidal dissipation, and the transition
between them, should be explored further in more realistic models. A better
understanding of the interaction between convection and tidal flows is indeed
essential to correctly interpret observations of close binary stars and
short-period planetary orbits.
