Convective turbulent viscosity acting on equilibrium tidal flows: new frequency scaling of the effective viscosity

Tidal interactions are important in driving spin and orbital evolution in various astrophysical systems such as hot Jupiters, close binary stars and planetary satellites. However, the fluid dynamical mechanisms responsible for tidal dissipation in giant planets and stars remain poorly understood. One key mechanism is the interaction between tidal flows and turbulent convection which is thought to act as an eddy viscosity (ν_E) dampening the large scale tidal flow. The efficiency of this mechanism has long been debated, particularly in the regime of fast tides, when the tidal frequency (ω) exceeds the turnover frequency of the dominant convective eddies (ω_c). The pioneering work of Zahn (1966) proposed that ν_E ~ ω^-1 while Goldreich & Nicholson (1977) found ν_E ~ ω^-2. Using hydrodynamical simulations we investigate the dissipation of the large scale (non-wavelike) equilibrium tide as a result of its interaction with convection. Our approach is to conduct a wide parameter survey in order to study the interaction between an oscillatory background shear flow, which represents a large-scale tidal flow, and the convecting fluid inside a small patch of a star or planet. We simulate Rayleigh-Bénard convection in this Cartesian model and explore how the effective viscosity of the turbulence depends on the tidal (shear) frequency. We will present the results from our simulations to determine the effective viscosity, and its dependence on the tidal frequency in both laminar and weakly turbulent regimes. The main result is a new scaling law for the frequency dependence of the effective viscosity which has not previously been observed in simulations or predicted by theory and occurs for shear frequencies smaller than those in the fast tides regime. These results have important implications for tidal dissipation in convection zones of stars and planets, and indicate that the classical tidal theory of the equilibrium tide in stars and giant planets should be revisited.