Wave propagation in semiconvective regions of giant planets

Abstract

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.

Convective turbulent viscosity acting on equilibrium tidal flows: new frequency scaling of the effective viscosity

“…Wu 2005;Ogilvie & Lin 2007;Goodman & Lackner 2009;Papaloizou & Ivanov 2010;Favier et al 2014;Barker 2016), and this mechanism may be important for tidal circularisation and spin synchronisation. In giant planets, the role of stably-stratified (or semi-convective) layers is also being explored (Fuller et al 2016;André et al 2017;André et al 2019;Pontin et al 2020) with possible application to the orbital migration of the moons of Jupiter and Saturn (e.g. Lainey et al 2009Lainey et al , 2012Lainey et al , 2017Lainey et al , 2020.…”

Enhancement of wave transmissions in multiple radiative and convective zones

“…(2017) and Pontin et al. (2020). A useful approach to modelling wave propagations in a multi-layer structure is to build on relations of wave amplitudes by transfer matrices.…”

“…Conditions on 'resonant propagation' and 'resonant tunnelling' have been provided. Pontin et al (2020) have conducted interesting research on wave propagation in a multi-layer structure in a non-rotating sphere, and found that wave transmissions are efficient for very large wavelength waves. This already shares some similarities with our analysis on the tunnelling of gravity waves in the f -plane.…”

“…We choose q m > 0 for C > 0, and q m < 0 for C < 0. Wave propagations in multi-layer structures have been investigated in Belyaev et al (2015), André et al (2017) and Pontin et al (2020). A useful approach to modelling wave propagations in a multi-layer structure is to build on relations of wave amplitudes by transfer matrices.…”

“…They also discovered that perfect wave transmission can be obtained at the critical latitude. Pontin et al (2020) studied the wave propagation in semiconvective regions of non-rotating giant planets in the full sphere. They found that wave transmissions are efficient for very large wavelength waves.…”