Tidal dissipation due to the elliptical instability and turbulent viscosity in convection zones in rotating giant planets and stars

Abstract

Tidal dissipation in star-planet systems can occur through various mechanisms, among which is the elliptical instability. This acts on elliptically deformed equilibrium tidal flows in rotating fluid planets and stars, and excites inertial waves in convective regions if the dimensionless tidal amplitude (ε) is sufficiently large. We study its interaction with turbulent convection, and attempt to constrain the contributions of both elliptical instability and convection to tidal dissipation. For this, we perform an extensive suite of Cartesian hydrodynamical simulations of rotating Rayleigh-Bénard convection in a small patch of a planet. We find that tidal dissipation resulting from the elliptical instability, when it operates, is consistent with ε3, as in prior simulations without convection. Convective motions also act as an effective viscosity on large-scale tidal flows, resulting in continuous tidal dissipation (scaling as ε2). We derive scaling laws for the effective viscosity using (rotating) mixing-length theory, and find that they predict the turbulent quantities found in our simulations very well. In addition, we examine the reduction of the effective viscosity for fast tides, which we observe to scale with tidal frequency (ω) as ω−2. We evaluate our scaling laws using interior models of Hot Jupiters computed with MESA. We conclude that rotation reduces convective length scales, velocities and effective viscosities (though not in the fast tides regime). We estimate that elliptical instability is efficient for the shortest-period Hot Jupiters, and that effective viscosity of turbulent convection is negligible in giant planets compared with inertial waves.

Tidal Dissipation in Stably Stratified and Semiconvective Regions of Rotating Giant Planets: Incorporating Coriolis Forces

“…W are likely to be very small, on the order of 10 −15 or smaller using molecular values. It is not clear whether molecular values are appropriate though or whether tidal waves should be damped by turbulent diffusivities instead, which may be expected to be much larger (though still small, as discussed in, e.g., de Vries et al 2023). We assume ν and κ, and hence Pr, are constant in radius, and explore the widest range of these parameters that is computationally accessible, though we are unable to study values as small as the microscopic ones in planetary interiors-common with many other problems in astrophysics, thereby requiring us to understand how ν and κ affect our results before we can potentially extrapolate to real planets.…”

“…Such efficient rates of tidal dissipation are not currently understood theoretically, but have motivated an increasing number of works to explore tides in giant planets. Possible dissipative mechanisms that have been proposed include inertial waves (restored by Coriolis forces) in convective regions (Ogilvie & Lin 2004;Wu 2005;Goodman & Lackner 2009), gravity or gravito-inertial waves in stable layers (restored by buoyancy forces, and also by rotation) which might be locked in resonance (Fuller et al 2016), and interactions of equilibrium tides with turbulent convection, though the latter mechanism is not widely believed to be important and is more uncertain (Goldreich & Nicholson 1977;Duguid et al 2020;Barker & Astoul 2021;Terquem 2021;de Vries et al 2023). Finally, dissipation in the viscoelastic rocky/ icy cores of giant planets have also been proposed to be important (e.g., Remus et al 2012Remus et al , 2015Storch & Lai 2014Lainey et al 2017), and are worthy of future study, even if fluid mechanisms are typically favored currently due to the instability and mixing of such cores in the hightemperature and high-pressure environments near the centers of giant planets.…”