An analytical framework for atmospheric tides on rocky planets. I. Formulation

TL;DR

This paper develops an analytical model to understand atmospheric thermal tides on rocky planets, focusing on their influence on planetary rotation and resonance effects, with implications for planets like Venus and early Earth.

Contribution

It introduces a new linear analytical framework for atmospheric response to tidal forcings, encompassing both isothermal and isentropic profiles, including dissipative effects.

Findings

Derived explicit expressions for tidal fields in spherical atmospheres.

Unified treatment of isothermal and isentropic atmospheric cases.

Foundation for future analytical and numerical studies of thermotidal torque.

Abstract

Atmospheric thermal tides arise from the diurnal contrast in stellar irradiation. They exert a significant influence on the long-term rotational evolution of rocky planets because they can accelerate the planetary spin, thereby counteracting the decelerating effect of classical gravitational tides. Consequently, equilibrium tide-locked states may emerge, as exemplified by Venus and hypothesised for Precambrian Earth. Quantifying the atmospheric thermal torque and elucidating its dependence on tidal frequency -- both in the low- and high-frequency regimes -- is therefore essential. In particular, we focus here on the resonance that affected early Earth, which is associated with a forced Lamb wave. Within the framework of linear theory, we develop a new analytical model of the atmospheric response to both gravitational an thermal tidal forcings for two representative vertical temperature profiles that bracket the atmospheres of rocky planets: (i) an isothermal profile (uniform temperature) and (ii) an isentropic profile (uniform potential temperature). Dissipative processes are incorporated via Newtonian cooling. We demonstrate that the isothermal and isentropic cases are governed by the same general closed-form solution, and we derive explicit expressions for the three-dimensional tidal fields (pressure, temperature, density and wind velocities) throughout the spherical atmospheric shell. These results constitute the foundation for two forthcoming papers, in which analytical formulae for the thermotidal torque will be presented and compared with numerical solutions obtained from General Circulation Models (GCMs).