Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-12-03T00:38:34.188Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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

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.)

References

Budd, W. F., Jacka, T. H. & Morgan, V. I. 1980 Antarctic iceberg melt rates derived from size distributions and movement rates. Ann. Glaciol. 1, 103–112.Google Scholar
Carey, V. P. & Gebhart, B. 1982 Transport near a vertical ice surface melting in saline water: experiments at low salinities. J. Fluid Mech. 117, 403–423.Google Scholar
Cenedese, C. & Gatto, V. M. 2016 Impact of a localized source of subglacial discharge on the heat flux and submarine melting of a tidewater glacier: a laboratory study. J. Phys. Oceanogr. 46, 3155–3163.Google Scholar
Dutrieux, P., Stewart, C., Jenkins, A., Nicholls, K. W., Corr, H. F. J., Rignot, E. & Steffen, K. 2014 Basal terraces on melting ice shelves. Geophys. Res. Lett. 41, 5506–5513.Google Scholar
Dutrieux, P., Vaughan, D. G., Corr, H. F. J., Jenkins, A., Holland, P. R., Joughin, L. & Fleming, A. H. 2013 Pine Island glacier ice shelf melt distributed at kilometre scales. The Cryosphere 7, 1543–1555.CrossRefGoogle Scholar
Fujii, T. & Imura, H. 1972 Natural-convection heat transfer from a plate with arbitrary inclination. Intl J. Heat Mass Transfer 15, 765–767.Google Scholar
Holland, D. M. & Jenkins, A. 1999 Modelling thermodynamic ice-ocean interactions at the base of an ice shelf. J. Phys. Oceanogr. 29, 1787–1800.2.0.CO;2>CrossRefGoogle Scholar
Holman, J. P. 2010 Heat Transfer, 10th edn. McGraw-Hill.Google Scholar
Howard, L. N. 1966 Convection at high Reynolds number. In Proceedings of the 11th International Congress of Applied Mechanics (ed. Görtler, H.), pp. 1109–1115.Google Scholar
Huppert, H. E. 1990 The fluid mechanics of solidification. J. Fluid Mech. 212, 209–240.Google Scholar
IOC, SCOR & IAPSO2010 The International Thermodynamic Equation of Seawater – 2010: Calculation and Use of Thermodynamic Properties. Intergovernmental Oceanographic Commision, Manuals and Guides No. 89.Google Scholar
Jenkins, A. 2011 Convection-driven melting near the grounding lines of ice shelves and tidewater glaciers. J. Phys. Oceanogr. 41, 2279–2294.CrossRefGoogle Scholar
Jenkins, A., Dutrieux, P., McPhail, S. D., Perrett, J. R., Webb, A. T. & White, D. 2010 Observations beneath Pine Island Glacier in West Antarctica and implications for its retreat. Nat. Geosci. 3, 468–472.Google Scholar
Johnson, R. S. & Mollendorf, J. C. 1984 Transport from a vertical ice surface melting in saline water. Intl J. Heat Mass Transfer 27 (10), 1928–1932.CrossRefGoogle Scholar
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.Google Scholar
Kerr, R. C. 1994a Melting driven by vigorous compositional convection. J. Fluid Mech. 280, 255–285.CrossRefGoogle Scholar
Kerr, R. C. 1994b Dissolving driven by vigorous compositional convection. J. Fluid Mech. 280, 287–302.Google Scholar
Kerr, R. C. & McConnochie, C. D. 2015 Dissolution of a vertical solid surface by turbulent compositional convection. J. Fluid Mech. 765, 211–228.CrossRefGoogle Scholar
Lick, W. 1965 The instability of a fluid layer with time-dependent heating. J. Fluid Mech. 21, 565–576.CrossRefGoogle Scholar
McConnochie, C. D. & Kerr, R. C. 2016 The effect of a salinity gradient on the dissolution of a vertical ice face. J. Fluid Mech. 791, 589–607.Google Scholar
McConnochie, C. D. & Kerr, R. C. 2017 Enhanced ablation of a vertical ice face due to an external freshwater plume. J. Fluid Mech. 810, 429–447.CrossRefGoogle Scholar
Rignot, E., Jacobs, S., Mouginot, J. & Scheuchl, B. 2013 Ice shelf melting around Antarctica. Science 341, 266–270.Google Scholar
Rignot, E., Velicogna, I., van den Broeke, M. R., Monaghan, A. & Lenaerts, J. T. M. 2011 Acceleration of the contribution of the Greenland and Antarctic ice sheets to sea level rise. Geophys. Res. Lett. 38, L05503.Google Scholar
Sharqawy, M. H., Lienhard, V. J. H. & Zubair, S. M. 2010 Thermophysical properties of seawater: a review of existing correlations and data. Desal. Water Treat. 16, 354–380.Google Scholar
Shepherd, A., Wingham, D. & Rignot, E. 2004 Warm ocean is eroding West Antarctic Ice Sheet. Geophys. Res. Lett. 31, L23402.CrossRefGoogle Scholar
Stanton, T. P., Shaw, W. J., Truffer, M., Corr, H. F. J., Peters, L. E., Riverman, K. L., Bindschadler, R., Holland, D. M. & Anandakrishan, S. 2013 Channelized ice melting in the ocean boundary layer beneath Pine Island Glacier, Antarctica. Science 341, 1236–1239.Google Scholar
Vliet, G. C. & Ross, D. C. 1975 Turbulent natural convection on upward and downward facing inclined constant heat flux surfaces. J. Heat Transfer 97, 549–555.CrossRefGoogle Scholar
Wells, A. J. & Worster, M. G. 2011 Melting and dissolving of a vertical solid surface with laminar compositional convection. J. Fluid Mech. 687, 118–140.CrossRefGoogle Scholar
Woods, A. W. 1992 Melting and dissolving. J. Fluid Mech. 239, 429–448.Google Scholar