The influence of convection on tidal flows

Tidal interactions are important in driving spin and orbital evolution in various astrophysical systems such as hot Jupiters, close binary stars, planetary satellites, and more. 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 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 exceeds the turnover frequency of the dominant convective eddies. The pioneering work of Zahn (1966) proposed that the effective viscosity scales as the inverse of the tidal frequency while Goldreich & Nicholson (1977) found that the effective viscosity scales as the inverse squared of the tidal frequency.

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 (over a number of parameters) 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 depends on the tidal (shear) frequency in both laminar and turbulent regimes. We also provide a complementary asymptotic analysis which is an extension of the work of Ogilvie & Lesur (2012) which supports our findings in the laminar cases.

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 results are: 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; the possibility of anti-dissipation (which could result in inverse-tides); and a strong agreement with the frequency dependence of Goldreich & Nicholson (1977) (despite disagreement with the fundamental mechanism).

These results have important implications for tidal dissipation in convection zones of stars and planets which we will discuss. The results of this work indicate that the classical tidal theory of the equilibrium tide in stars and giant planets should be revisited.