Efficiency of Tidal Dissipation in Convective Flow Under Rapid Tidal Forcing

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Original abstract

For close binaries and star-planet systems, tidal interactions mediate the energy transfer between the orbital motion and the internal flows of the bodies involved, thus playing a central role in their evolution. For equilibrium tides, the associated energy transfer is commonly modeled through an effective viscosity acting on the tidal flow. However, the scaling of viscous dissipation efficiency with tidal frequency $ω_\text{T}$ remains debated, particularly when $ω_\text{T}$ greatly exceeds the convective eddy turnover frequency $ω_\text{c}$. Previous numerical studies have addressed this issue by subjecting a turbulent convective flow to an oscillating background shear mimicking equilibrium tides. In this work, we adopt a novel three-layered convective box -- designed to represent a stellar convection zone sandwiched between two stable layers -- driven by an external periodic forcing. We quantify tidal dissipation efficiency by the forcing power on the flow in steady state. Our results yield a shallower scaling of tidal power per unit mass with $ω_\text{T}$ than reported in earlier shear-flow simulations. This scaling is consistent with the prediction by \cite{Terquem2021}, suggesting that the effective turbulent viscosity depends only weakly on $ω_\text{T}$, although our simulations are restricted to $ω_\text{T}\lesssim 10ω_\text{c}$. Moreover, we find no evidence of inverse energy transfer (or ``negative viscosity''), a phenomenon observed in some prior shear-flow simulations. We further investigate the influence of rotation within the same local framework. Slow rotation ($Ω\lesssim ω_\text{T}$) tends to enhance the tidal power, whereas fast rotation ($Ω\gtrsimω_\text{T}$) significantly suppresses it. We discuss the limitations of our approach and the broader implications of our findings.

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