Tidally Excited Inertial Waves in Stars and Planets: Exploring the Frequency-dependent and Averaged Dissipation with Nonlinear Simulations

Abstract

We simulate the nonlinear hydrodynamical evolution of tidally excited inertial waves in convective envelopes of rotating stars and giant planets modeled as spherical shells containing incompressible, viscous, and adiabatically stratified fluid. This model is relevant for studying tidal interactions between close-in planets and their stars, as well as close low-mass star binaries. We explore in detail the frequency-dependent tidal dissipation rates obtained from an extensive suite of numerical simulations, which we compare with linear theory, including with the widely employed frequency-averaged formalism to represent inertial wave dissipation. We demonstrate that the frequency-averaged predictions appear to be quite robust and are approximately reproduced in our nonlinear simulations spanning the frequency range of inertial waves as we vary the convective envelope thickness, tidal amplitude, and Ekman number. Yet, we find nonlinear simulations can produce significant differences with linear theory for a given tidal frequency (potentially by orders of magnitude), largely due to tidal generation of differential rotation and its effects on the waves. Since the dissipation in a given system can be very different both in linear and nonlinear simulations, the frequency-averaged formalism should be used with caution. Despite its robustness, it is also unclear how accurately it represents tidal evolution in real (frequency-dependent) systems.

An Efficient Tidal Dissipation Mechanism via Stellar Magnetic Fields

“…Many other proposed tidal dissipation mechanisms in stars with convective cores have been shown to be inefficient. These include convective turbulence acting on the large-scale equilibrium tide (e.g., Zahn 1966;Goldreich & Nicholson 1977;Ogilvie & Lesur 2012;Duguid et al 2019Duguid et al , 2020Vidal & Barker 2020a, 2020b; the elliptical instability (e.g., de Vries et al 2023); (linearly excited) inertial waves, which are not excited unless the tidal period is longer than half the stellar rotation period (e.g., Ogilvie & Lin 2007;Ivanov & Papaloizou 2010;Ogilvie 2013;Mathis 2015;Bolmont & Mathis 2016;Barker 2020;Astoul & Barker 2023); or resonance locking that typically operates on the stellar-evolution timescale, ∼Gyr (e.g., Ma & Fuller 2021). While recent work has explored alternative mechanisms for critical layer formation that would justify the fully damped IGW regime (e.g., by linear radiative damping; Guo et al 2023), the impact of magnetic fields on tidally excited IGWs remains unexplored to date.…”