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

Abstract

Turbulent convection is thought to act as an effective viscosity in damping equilibrium tidal flows, driving spin and orbital evolution in close convective binary systems. Compared to mixing-length predictions, this viscosity ought to be reduced when the tidal frequency |ωt| exceeds the turnover frequency ωcv of the dominant convective eddies, but the efficiency of this reduction has been disputed. We reexamine this long-standing controversy using direct numerical simulations of an idealized global model. We simulate thermal convection in a full sphere, and externally forced by the equilibrium tidal flow, to measure the effective viscosity νE acting on the tidal flow when |ωt|/ωcv ≳ 1. We demonstrate that the frequency reduction of νE is correlated with the frequency spectrum of the (unperturbed) convection. For intermediate frequencies below those in the turbulent cascade (|ωt|/ωcv ∼ 1 − 5), the frequency spectrum displays an anomalous 1/ωα power law that is responsible for the frequency-reduction νE∝1/|ωt|α, where α < 1 depends on the model parameters. We then get |νE|∝1/|ωt|δ with δ > 1 for higher frequencies, and δ = 2 is obtained for a Kolmogorov turbulent cascade. A generic |νE|∝1/|ωt|2 suppression is next found for higher frequencies within the dissipation range of the convection (but with negative values). Our results indicate that a better knowledge of the frequency spectrum of convection is necessary to accurately predict the efficiency of tidal dissipation in stars and planets resulting from this mechanism.

Triadic resonances driven by thermal convection in a rotating sphere

“…In stars and giant planets, the interaction between convection and tides is of great importance for calculating the efficiency of tidal dissipation, yet the problem remains poorly understood (Ogilvie 2014). Turbulent convection is usually treated as an effective viscosity in damping the tidal flow (Zahn 1989; Vidal & Barker 2020). However, given small in the convective zone of rotating stars and giant planets, both convection and tides can drive inertial waves, which would be interacting simultaneously and make it more difficult to estimate the efficiency of tidal dissipation in these systems.…”

Tidal dissipation in evolving low-mass and solar-type stars with predictions for planetary orbital decay

“…In convection zones, we compute convective damping of equilibrium tides, accounting for the frequency dependence of the effective turbulent viscosity (e.g. Duguid et al 2020b;Vidal & Barker 2020b). We compute dissipation of IWs (dynamical tides) in convection zones using a frequencyaveraged formalism (Ogilvie 2013) that accounts for the realistic structure of the star for the first time.…”

“…This appears to hold for a wide range of Rayleigh numbers in a local model of convection, but the simulations also indicate a possible tidal amplitude dependence for ω/ω c 1, which we do not explore further here. We caution though that the intermediate regime may be somewhat model dependent (Vidal & Barker 2020b). Note that ν FIT matches the scaling of ν GN at high frequencies, but with a different proportionality constant that implies more efficient dissipation.…”

On the interaction between fast tides and convection

“…The interaction between equilibrium tides and convection is therefore likely to be dominated by terms considered in previous Boussinesq models (e.g. Ogilvie & Lesur 2012;Duguid et al 2020b;Vidal & Barker 2020a). These usually indicate weak dissipation of equilibrium tides, such that tidal dissipation in pre-and main-sequence stars and giant planets is probably instead due to inertial and internal gravity waves (e.g.…”