Scaling laws to understand tidal dissipation in fluid planetary regions and stars I. Rotation, stratification and thermal diffusivity^⋆

¹ IMCCE, Observatoire de Paris, CNRS UMR 8028, 77 avenue Denfert-Rochereau, 75014 Paris, France
e-mail: pierre.auclair-desrotour@obspm.fr
² Laboratoire AIM Paris-Saclay, CEA/DSM−CNRS−Université Paris-Diderot, IRFU/SAp Centre de Saclay, 91191 Gif-sur-Yvette, France
³ LESIA, Observatoire de Paris, CNRS UMR 8109, UPMC, Université Paris-Diderot, 5 place Jules Janssen, 92195 Meudon, France
e-mail: stephane.mathis@cea.fr
⁴ SYRTE, Observatoire de Paris, CNRS UMR 8630, UPMC, LNE, 61 avenue de l’Observatoire, 75014 Paris, France
e-mail: christophe.leponcin@obspm.fr

Received: 2 April 2015
Accepted: 16 June 2015

Abstract

Context. Tidal dissipation in planets and stars is one of the key physical mechanisms driving the evolution of star-planet and planet-moon systems. Several signatures of its action are observed in planetary systems thanks to their orbital architecture and the rotational state of their components.

Aims. Tidal dissipation inside the fluid layers of celestial bodies is intrinsically linked to the dynamics and physical properties of those bodies. This complex dependence must be characterized.

Methods. We compute the tidal kinetic energy dissipated by viscous friction and thermal diffusion in a rotating local fluid Cartesian section of a star, planet, or moon submitted to a periodic tidal forcing. The properties of tidal gravito-inertial waves excited by the perturbation are derived analytically as explicit functions of the tidal frequency and local fluid parameters (i.e. the rotation, the buoyancy frequency characterizing the entropy stratification, viscous and thermal diffusivities) for periodic normal modes.

Results. The sensitivity of the resulting dissipation frequency-spectra, which could be highly resonant, to a control parameter of the system is either important or negligible depending on the position in the regime diagram relevant for planetary and stellar interiors. For corresponding asymptotic behaviours of tidal gravito-inertial waves dissipated by viscous friction and thermal diffusion, scaling laws for the frequencies, number, width, height, and contrast with the non-resonant background of resonances are derived to quantify these variations.

Conclusions. We characterize the strong impact of the internal physics and dynamics of fluid planetary layers and stars on the dissipation of tidal kinetic energy in their bulk. We point out the key control parameters that really play a role in tidal dissipation and demonstrate how it is now necessary to develop ab initio modelling for tidal dissipation in celestial bodies.