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Dissolution of a sloping solid surface by turbulent compositional convection

Published online by Cambridge University Press:  08 May 2018

Craig D. McConnochie Open the ORCID record for Craig D. McConnochie [Opens in a new window]  and
Ross C. Kerr
Craig D. McConnochie*
Affiliation:
Research School of Earth Sciences, The Australian National University, Canberra, ACT 2601, Australia
Ross C. Kerr
Affiliation:
Research School of Earth Sciences, The Australian National University, Canberra, ACT 2601, Australia
*
†Email address for correspondence: cmcconnochie@whoi.edu
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Abstract

We examine the dissolution of a sloping solid surface driven by turbulent compositional convection. The scaling analysis presented by Kerr & McConnochie (J. Fluid Mech., vol. 765, 2015, pp. 211–228) for the dissolution of a vertical wall is extended to the case of a sloping wall. The model has no free parameters and no dependence on height. It predicts that while the interfacial temperature and interfacial composition are independent of the slope, the dissolution velocity is proportional to $\cos ^{2/3}\unicode[STIX]{x1D703}$ , where $\unicode[STIX]{x1D703}$ is the angle of the sloping surface to the vertical. The analysis is tested by comparing it with laboratory measurements of the ablation of a sloping ice wall in contact with salty water. We apply the model to make predictions of the turbulent convective dissolution of a sloping ice shelf in the polar oceans.

JFM classification

Geophysical and Geological Flows: Ice sheets Phase change: Solidification/melting Turbulent Flows: Turbulent convection

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 846 , 10 July 2018 , pp. 563 - 577
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Copyright
© 2018 Cambridge University Press 

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