Ice formation in the Arctic during summer: false-bottoms

TL;DR

This paper develops a mathematical model for false-bottom ice formation in the Arctic summer, analyzing the growth and melting processes governed by heat and salt fluxes using a two-phase Stefan problem framework.

Contribution

It introduces a novel mathematical model for false-bottom ice dynamics and proves the existence and uniqueness of solutions for this complex free boundary problem.

Findings

Established a mathematical framework for false-bottom ice formation.

Proved existence and uniqueness of solutions to the model.

Provides insights into heat and salt flux interactions in ice growth and ablation.

Abstract

The only source of ice formation in the Arctic during summer is a layer of ice called false-bottoms between an under-ice melt pond and the underlying ocean. Of interest is to give a mathematical model in order to determine the simultaneous growth and ablation of false-bottoms, which is governed by both of heat fluxes and salt fluxes. In one dimension, this problem may be considered mathematically as a two-phase Stefan problem with two free boundaries. Our main result is to prove the existence and uniqueness of the solution from the initial condition.