Abstract
We study how stably stratified or semi-convective layers alter the tidal dissipation rates associated with the generation of internal waves in planetary interiors. We consider if these ...layers could contribute to the high rates of tidal dissipation observed for Jupiter and Saturn in our solar system. We use an idealized global spherical Boussinesq model to study the influence of stable stratification and semi-convective layers on tidal dissipation rates. We carry out analytical and numerical calculations considering realistic tidal forcing and measure how the viscous and thermal dissipation rates depend on the parameters relating to the internal stratification profile. We find that the strongly frequency-dependent tidal dissipation rate is highly dependent on the parameters relating to the stable stratification, with strong resonant peaks that align with the internal modes of the system. The locations and sizes of these resonances depend on the form and parameters of the stratification, which we explore both analytically and numerically. Our results suggest that stable stratification can significantly enhance the tidal dissipation in particular frequency ranges. Analytical calculations in the low-frequency regime give us scaling laws for the key parameters, including the tidal quality factor
Q
′
due to internal gravity waves. Stably stratified layers can significantly contribute to tidal dissipation in solar and extrasolar giant planets, and we estimate substantial tidal evolution for hot Neptunes. Further investigation is needed to robustly quantify the significance of the contribution in realistic interior models, and to consider the contribution of inertial waves.
Abstract
We study how stably stratified or semiconvective layers alter tidal dissipation rates associated with the generation of inertial, gravito-inertial, interfacial, and surface gravity waves in ...rotating giant planets. We explore scenarios in which stable (nonconvective) layers contribute to the high rates of tidal dissipation observed for Jupiter and Saturn in our solar system. Our model is an idealized spherical Boussinesq system incorporating Coriolis forces to study effects of stable stratification and semiconvective layers on tidal dissipation. Our detailed numerical calculations consider realistic tidal forcing and compute the resulting viscous and thermal dissipation rates. The presence of an extended stably stratified fluid core significantly enhances tidal wave excitation of both inertial waves (due to rotation) in the convective envelope and gravito-inertial waves in the dilute core. We show that a sufficiently strongly stratified fluid core enhances inertial wave dissipation in a convective envelope much like a solid core does. We demonstrate that efficient tidal dissipation rates (and associated tidal quality factors
Q
′
)—sufficient to explain the observed migration rates of Saturn's moons—are predicted at the frequencies of the orbiting moons due to the excitation of inertial or gravito-inertial waves in our models with stable layers (without requiring resonance locking). Stable layers could also be important for tidal evolution of hot and warm Jupiters and hot Neptunes, providing efficient tidal circularization rates. Future work should study more sophisticated planetary models that also account for magnetism and differential rotation, as well as the interaction of inertial waves with turbulent convection.
We study how stably stratified or semi-convective layers alter tidal dissipation rates associated with the generation of inertial, gravito-inertial, interfacial and surface gravity waves in rotating ...giant planets. We explore scenarios in which stable (non-convective) layers contribute to the high rates of tidal dissipation observed for Jupiter and Saturn in our solar system. Our model is an idealised spherical Boussinesq system incorporating Coriolis forces to study effects of stable stratification and semi-convective layers on tidal dissipation. Our detailed numerical calculations consider realistic tidal forcing and compute the resulting viscous and thermal dissipation rates. The presence of an extended stably stratified fluid core significantly enhances tidal wave excitation of both inertial waves (due to rotation) in the convective envelope and gravito-inertial waves in the dilute core. We show that a sufficiently strongly stratified fluid core enhances inertial wave dissipation in a convective envelope much like a solid core does. We demonstrate that efficient tidal dissipation rates (and associated tidal quality factors \(Q'\)) -- sufficient to explain the observed migration rates of Saturn's moons -- are predicted at the frequencies of the orbiting moons due to the excitation of inertial or gravito-inertial waves in our models with stable layers (without requiring resonance-locking). Stable layers could also be important for tidal evolution of hot and warm Jupiters, and hot Neptunes, providing efficient tidal circularisation rates. Future work should study more sophisticated planetary models that also account for magnetism and differential rotation, as well as the interaction of inertial waves with turbulent convection.
We study how stably stratified or semi-convective layers alter the tidal dissipation rates associated with the generation of internal waves in planetary interiors. We consider if these layers could ...contribute to the high rates of tidal dissipation observed for Jupiter and Saturn in our solar system. We use an idealised global spherical Boussinesq model to study the influence of stable stratification and semi-convective layers on tidal dissipation rates. We carry out analytical and numerical calculations considering realistic tidal forcing and measure how the viscous and thermal dissipation rates depend on the parameters relating to the internal stratification profile. We find that the strongly frequency-dependent tidal dissipation rate is highly dependent on the parameters relating to the stable stratification, with strong resonant peaks that align with the internal modes of the system. The locations and sizes of these resonances depend on the form and parameters of the stratification, which we explore both analytically and numerically. Our results suggest that stable stratification can significantly enhance the tidal dissipation in particular frequency ranges. Analytical calculations in the low frequency regime give us scaling laws for the key parameters, including the tidal quality factor \(Q'\) due to internal gravity waves. Stably stratified layers can significantly contribute to tidal dissipation in solar and extrasolar giant planets, and we estimate substantial tidal evolution for hot Neptunes. Further investigation is needed to robustly quantify the significance of the contribution in realistic interior models, and to consider the contribution of inertial waves.
Recent observations of Jupiter and Saturn suggest that heavy elements may be diluted in the gaseous envelope, providing a compositional gradient that could stabilise ordinary convection and produce a ...stably-stratified layer near the core of these planets. This region could consist of semi-convective layers with a staircase-like density profile, which have multiple convective zones separated by thin stably-stratified interfaces, as a result of double-diffusive convection. These layers could have important effects on wave propagation and tidal dissipation that have not been fully explored. We analyse the effects of these layers on the propagation and transmission of internal waves within giant planets, extending prior work in a local Cartesian model. We adopt a simplified global Boussinesq planetary model in which we explore the internal waves in a non-rotating spherical body. We begin by studying the free modes of a region containing semi-convective layers. We then analyse the transmission of internal waves through such a region. The free modes depend strongly on the staircase properties, and consist of modes with both internal and interfacial gravity wave-like behaviour. We determine the frequency shifts of these waves as a function of the number of steps to explore their potential to probe planetary internal structures. We also find that wave transmission is strongly affected by the presence of a staircase. Very large-wavelength waves are transmitted efficiently, but small-scale waves are only transmitted if they are resonant with one of the free modes. The effective size of the core is therefore larger for non-resonant modes.
