Convection in a mushy-layer along a heated wall

TL;DR

This paper investigates boundary-layer convection in a mushy layer along a heated wall, combining theoretical analysis and numerical simulations to identify four distinct regions and their behaviors, with implications for natural phenomena like sea ice and volcanic zones.

Contribution

It provides a novel theoretical and numerical framework for understanding convection patterns in mushy layers with four distinct regions, advancing knowledge of their structure and dynamics.

Findings

Four distinct regions identified in the mushy layer convection.

Numerical simulations confirm theoretical scalings and predictions.

Convection behavior resembles a buoyant plume with implications for melting processes.

Abstract

Motivated by the mushy zones of sea ice, volcanoes, and icy moons of the outer solar system, we perform a theoretical and numerical study of boundary-layer convection along a vertical heated wall in a bounded ideal mushy region. The mush is comprised of a porous and reactive binary alloy with a mixture of saline liquid in a solid matrix, and is studied in the near-eutectic approximation. Here we demonstrate the existence of four regions and study their behavior asymptotically. Starting from the bottom of the wall, the four regions are (i) an isotropic corner region; (ii) a buoyancy dominated vertical boundary layer; (iii) an isotropic connection region; and (iv) a horizontal boundary layer at the top boundary with strong gradients of pressure and buoyancy. Scalings from numerical simulations are consistent with the theoretical predictions. Close to the heated wall, the convection in the mushy layer is similar to a rising buoyant plume abruptly stopped at the top, leading to increased pressure and temperature in the upper region, whose impact is discussed as an efficient melting mechanism.