Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-28T23:59:00.200Z Has data issue: false hasContentIssue false
  • English
  • Français

Melting and dissolving of a vertical solid surface with laminar compositional convection

Published online by Cambridge University Press:  06 October 2011

Andrew J. Wells  and
M. Grae Worster
Andrew J. Wells*
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
M. Grae Worster
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider laminar compositional convection of buoyant melt released by ablation of a vertical solid surface into a two-component fluid. Asymptotic solutions are used to describe separate cases: the ablation rate is either controlled by thermal transport, corresponding to melting, or by solutal transport, corresponding to dissolution. Melting is faster and generates a stronger flow than dissolving. We determine the temperature and solute concentration conditions leading to either melting or dissolving and find that these conditions do not vary with the strength of the buoyancy that drives convective flow.

JFM classification

Boundary Layers: Boundary layer structure Convection: Buoyant boundary layers Phase change: Solidification/melting
Type
Papers
Information
Journal of Fluid Mechanics , Volume 687 , 25 November 2011 , pp. 118 - 140
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

‡

Present address: Department of Geology and Geophysics, Yale University, New Haven, CT 06520, USA.

References

1. Acton, F. S. 1990 Numerical Methods that Work. MAA.CrossRefGoogle Scholar
2. Carey, V. P. & Gebhart, B. 1982a Transport near a vertical ice surface melting in saline water: some numerical calculations. J. Fluid Mech. 117, 379–402.CrossRefGoogle Scholar
3. Carey, V. P. & Gebhart, B. 1982b Transport near a vertical ice surface melting in saline water: experiments at low salinities. J. Fluid Mech. 117, 403–423.CrossRefGoogle Scholar
4. Gebhart, B., Jaluria, Y., Mahajan, R. L. & Sammakia, B. 1988 Buoyancy Induced Flows and Transport, pp. 547–655 Hemisphere, ch. 11.Google Scholar
5. Josberger, E. G. & Martin, S. 1981 A laboratory and theoretical study of the boundary layer adjacent to a vertical melting ice wall in salt water. J. Fluid Mech. 111, 439–473.CrossRefGoogle Scholar
6. Kerr, R. C. 1994a Melting driven by vigorous compositional convection. J. Fluid Mech. 280, 255–285.CrossRefGoogle Scholar
7. Kerr, R. C. 1994b Dissolving driven by vigorous compositional convection. J. Fluid Mech. 280, 287–302.CrossRefGoogle Scholar
8. Kuiken, H. K. 1968 An asymptotic solution for large Prandtl number free convection. J. Engng Maths 2 (4), 355–371.CrossRefGoogle Scholar
9. Morgan, V. I. & Budd, W. F. 1978 The distribution, movement and melt rates of Antarctic icebergs. In Iceberg Utilization: Proceedings of the First International Conference. (ed. Husseiny, A. ). pp. 220–228. Pergamon Press.CrossRefGoogle Scholar
10. Nilson, R. H. 1985 Countercurrent convection in a double diffusive boundary layer. J. Fluid Mech. 160, 181–210.CrossRefGoogle Scholar
11. Notz, D., McPhee, M. G., Worster, M. G., Maykut, G. A., Schlünzen, K. H. & Eicken, H. 2003 Impact of underwater–ice evolution on Arctic summer sea ice. J. Geophys. Res. 108, 16–1–16–12.CrossRefGoogle Scholar
12. Perovich, D. K., Richter-Menge, J. A., Jones, K. F. & Light, B. 2008 Sunlight, water and ice: extreme arctic sea ice melt during the summer of 2007. Geophys. Res. Lett. 35, doi:10.1029/2008GL034007.CrossRefGoogle Scholar
13. Woods, A. W. 1992 Melting and dissolving. J. Fluid Mech. 239, 429–448.CrossRefGoogle Scholar