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Convection in a mushy layer along a vertical heated wall

Published online by Cambridge University Press:  14 September 2021

S. Boury*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
C.R. Meyer
Affiliation:
Thayer School of Engineering, Dartmouth College, 14 Engineering Drive, Hanover, NH 03755, USA
G.M. Vasil
Affiliation:
School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales 2006, Australia
A.J. Wells
Affiliation:
Atmospheric, Oceanic and Planetary Physics, Department of Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
*
Email address for correspondence: sb7918@nyu.edu

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 behaviour 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.

Type
JFM Papers
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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