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

Tidally-excited inertial waves in stars and planets: exploring the frequency-dependent and averaged dissipation with nonlinear simulations