The Stefan problem with mushy region as a scaling limit of stochastic PDE with turbulent transport

TL;DR

This paper proves that solutions to stochastic Stefan problems with turbulent transport converge to deterministic PDE solutions, revealing turbulence's role in accelerating ice melting.

Contribution

It introduces a scaling limit theorem for the Stefan problem with a mushy region, connecting stochastic turbulent models to deterministic PDEs.

Findings

Turbulence accelerates ice melting in the model

Stochastic solutions converge to deterministic PDE solutions

Provides a rigorous mathematical framework for turbulent phase-change modeling

Abstract

This work establishes a scaling limit theorem for the Stefan problem incorporating a mushy region, demonstrating that solutions to stochastic variants with turbulent transport terms converge to the solution to a deterministic partial differential equation. The analysis builds upon recent advances in stochastic phase-change modeling and turbulent flow mathematics in [5]. In the physical interpretation of an ice melting process, our result shows that turbulence accelerates ice melting.