Ocean Circulation on Tide-locked Lava Worlds, Part II: Scalings

TL;DR

This paper develops and validates scaling laws for magma ocean circulation on tidally locked lava planets, revealing how external forcings and planetary parameters influence ocean depth and flow regimes.

Contribution

It introduces new scaling laws for magma ocean dynamics across different regimes, supported by numerical simulations and applied to lava super-Earths.

Findings

Magma ocean depth ranges from meters to hundreds of meters.

Scaling laws accurately predict oceanic flow characteristics in different regimes.

Most lava super-Earths likely have rotation-dominant magma oceans.

Abstract

On tidally locked lava planets, magma ocean can form on the permanent dayside. The circulation of the magma ocean can be driven by stellar radiation and atmospheric winds. The strength of ocean circulation and the depth of the magma ocean depend on external forcings and the dominant balance of the momentum equation. In this study, we develop scaling laws for the magma ocean depth, oceanic current speed, and ocean heat transport convergence driven by stellar and wind forcings in three different dynamic regimes: non-rotating viscosity-dominant Regime I, non-rotating inviscid limit Regime II, and rotation-dominant Regime III. Scaling laws suggest that magma ocean depth, current speed, and ocean heat transport convergence are controlled by various parameters, including vertical diffusivity/viscosity, substellar temperature, planetary rotation rate, and wind stress. In general, scaling laws predict that magma ocean depth ranges from a few meters to a few hundred meters. For Regime I, results from scaling laws are further confirmed by numerical simulations. Considering the parameters of a typical lava super-Earth, we found that the magma ocean is most likely in the rotation-dominant Regime III.