Scaling laws for ablation waves formed by ice sublimation and rock dissolution: applications to the Earth, Mars and Pluto

Abstract

Ablation waves involve solid substrate such as ice or soluble rocks. Ablation by sublimation or dissolution under turbulent winds or liquid flows may lead to the development of transverse linear bedforms (ablation waves) on volatile or soluble susbtrates. In glaciology, geomorphology, karstology and planetology, these ablation waves may provide relevant morphological markers to constrain the flows that control their formation. For that purpose, we describe a unified model, that couples mass transfers and turbulent flow dynamics and takes into account the relationship between the viscosity of the fluid and the diffusivity of the ablated material, for both sublimation and dissolution waves. From the stability analysis of the model, we derive three scaling laws that relate the wavelength, the migration velocity and the growth time of the waves to the physical characteristics (pressure, temperature, friction velocity, viscous length, ablation rate) of their environment through coefficients obtained numerically. The laws are validated on terrestrial examples and laboratory experiments of sublimation and dissolution waves. Then, these laws are plotted in specific charts for dissolution waves in liquid water, for sublimation waves in N2-rich atmospheres (e.g., Earth, Titan, Pluto) and in CO2-rich atmospheres (e.g., Mars, Venus). They are applied to rock dissolution on the walls of a limestone cave (Saint-Marcel d’Ardèche, France), to H2O ice sublimation on the North Polar Cap (Mars) and to CH4 ice sublimation in Sputnik Planitia (Pluto), to demonstrate how they can be used (1) either to derive physical conditions on planetary surfaces from observed geometric characteristics of ablation waves (2) or, conversely, to predict geometric characteristics of ablation waves from measured or inferred physical conditions on planetary surfaces. The migration of sublimation waves on regions of the Martian North Polar Cap and sublimation waves candidates on Pluto are discussed.