Skip to main content Accessibility help
×
Home

Dissolution of a sloping solid surface by turbulent compositional convection

  • Craig D. McConnochie (a1) and Ross C. Kerr (a1)

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.

Copyright

Corresponding author

Email address for correspondence: cmcconnochie@whoi.edu

References

Hide All
Budd, W. F., Jacka, T. H. & Morgan, V. I. 1980 Antarctic iceberg melt rates derived from size distributions and movement rates. Ann. Glaciol. 1, 103112.
Carey, V. P. & Gebhart, B. 1982 Transport near a vertical ice surface melting in saline water: experiments at low salinities. J. Fluid Mech. 117, 403423.
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, 31553163.
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, 55065513.
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, 15431555.
Fujii, T. & Imura, H. 1972 Natural-convection heat transfer from a plate with arbitrary inclination. Intl J. Heat Mass Transfer 15, 765767.
Holland, D. M. & Jenkins, A. 1999 Modelling thermodynamic ice-ocean interactions at the base of an ice shelf. J. Phys. Oceanogr. 29, 17871800.
Holman, J. P. 2010 Heat Transfer, 10th edn. McGraw-Hill.
Howard, L. N. 1966 Convection at high Reynolds number. In Proceedings of the 11th International Congress of Applied Mechanics (ed. Görtler, H.), pp. 11091115.
Huppert, H. E. 1990 The fluid mechanics of solidification. J. Fluid Mech. 212, 209240.
IOC, SCOR & IAPSO2010 The International Thermodynamic Equation of Seawater – 2010: Calculation and Use of Thermodynamic Properties. Intergovernmental Oceanographic Commision, Manuals and Guides No. 89.
Jenkins, A. 2011 Convection-driven melting near the grounding lines of ice shelves and tidewater glaciers. J. Phys. Oceanogr. 41, 22792294.
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, 468472.
Johnson, R. S. & Mollendorf, J. C. 1984 Transport from a vertical ice surface melting in saline water. Intl J. Heat Mass Transfer 27 (10), 19281932.
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, 439473.
Kerr, R. C. 1994a Melting driven by vigorous compositional convection. J. Fluid Mech. 280, 255285.
Kerr, R. C. 1994b Dissolving driven by vigorous compositional convection. J. Fluid Mech. 280, 287302.
Kerr, R. C. & McConnochie, C. D. 2015 Dissolution of a vertical solid surface by turbulent compositional convection. J. Fluid Mech. 765, 211228.
Lick, W. 1965 The instability of a fluid layer with time-dependent heating. J. Fluid Mech. 21, 565576.
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, 589607.
McConnochie, C. D. & Kerr, R. C. 2017 Enhanced ablation of a vertical ice face due to an external freshwater plume. J. Fluid Mech. 810, 429447.
Rignot, E., Jacobs, S., Mouginot, J. & Scheuchl, B. 2013 Ice shelf melting around Antarctica. Science 341, 266270.
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.
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, 354380.
Shepherd, A., Wingham, D. & Rignot, E. 2004 Warm ocean is eroding West Antarctic Ice Sheet. Geophys. Res. Lett. 31, L23402.
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, 12361239.
Vliet, G. C. & Ross, D. C. 1975 Turbulent natural convection on upward and downward facing inclined constant heat flux surfaces. J. Heat Transfer 97, 549555.
Wells, A. J. & Worster, M. G. 2011 Melting and dissolving of a vertical solid surface with laminar compositional convection. J. Fluid Mech. 687, 118140.
Woods, A. W. 1992 Melting and dissolving. J. Fluid Mech. 239, 429448.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed