Oceanic tides from Earth-like to ocean planets

¹ IMCCE, Observatoire de Paris, CNRS UMR 8028, PSL, 77 Avenue Denfert-Rochereau, 75014 Paris, France
e-mail: jacques.laskar@obspm.fr
² Laboratoire AIM Paris-Saclay, CEA/DRF - CNRS - Université Paris Diderot, IRFU/DAp Centre de Saclay, 91191 Gif-sur-Yvette, France
³ LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris Diderot, Sorbonne Paris Cité, 5 place Jules Janssen, 92195 Meudon, France
e-mail: stephane.mathis@cea.fr
⁴ Laboratoire d’Astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, 33615 Pessac, France
e-mail: pierre.auclair-desrotour@u-bordeaux.fr

Received: 7 November 2017
Accepted: 24 January 2018

Abstract

Context. Oceanic tides are a major source of tidal dissipation. They drive the evolution of planetary systems and the rotational dynamics of planets. However, two-dimensional (2D) models commonly used for the Earth cannot be applied to extrasolar telluric planets hosting potentially deep oceans because they ignore the three-dimensional (3D) effects related to the ocean’s vertical structure.

Aims. Our goal is to investigate, in a consistant way, the importance of the contribution of internal gravity waves in the oceanic tidal response and to propose a modelling that allows one to treat a wide range of cases from shallow to deep oceans.

Methods. A 3D ab initio model is developed to study the dynamics of a global planetary ocean. This model takes into account compressibility, stratification, and sphericity terms, which are usually ignored in 2D approaches. An analytic solution is computed and used to study the dependence of the tidal response on the tidal frequency and on the ocean depth and stratification.

Results. In the 2D asymptotic limit, we recover the frequency-resonant behaviour due to surface inertial-gravity waves identified by early studies. As the ocean depth and Brunt–Väisälä frequency increase, the contribution of internal gravity waves grows in importance and the tidal response becomes 3D. In the case of deep oceans, the stable stratification induces resonances that can increase the tidal dissipation rate by several orders of magnitude. It is thus able to significantly affect the evolution time scale of the planetary rotation.