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Ablation of sloping ice faces into polar seawater

  • Mainak Mondal (a1), Bishakhdatta Gayen (a1), Ross W. Griffiths (a1) and Ross C. Kerr (a1)


The effects of the slope of an ice–seawater interface on the mechanisms and rate of ablation of the ice by natural convection are examined using turbulence-resolving simulations. Solutions are obtained for ice slopes $\unicode[STIX]{x1D703}=2^{\circ }{-}90^{\circ }$ , at a fixed ambient salinity and temperature, chosen to represent common Antarctic ocean conditions. For laminar boundary layers the ablation rate decreases with height, whereas in the turbulent regime the ablation rate is found to be height independent. The simulated laminar ablation rates scale with $(\sin \unicode[STIX]{x1D703})^{1/4}$ , whereas in the turbulent regime it follows a $(\sin \unicode[STIX]{x1D703})^{2/3}$ scaling, both consistent with the theoretical predictions developed here. The reduction in the ablation rate with shallower slopes arises as a result of the development of stable density stratification beneath the ice face, which reduces turbulent buoyancy fluxes to the ice. The turbulent kinetic energy budget of the flow shows that, for very steep slopes, both buoyancy and shear production are drivers of turbulence, whereas for shallower slopes shear production becomes the dominant mechanism for sustaining turbulence in the convective boundary layer.


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Beckmann, A. & Goosse, H. 2003 A parameterization of ice shelf–ocean interaction for climate models. Ocean Model. 5 (2), 157170.10.1016/S1463-5003(02)00019-7
Budd, W. F., Jacka, T. H. & Morgan, V. I. 1980 Antarctic iceberg melt rates derived from size distributions and movement rates. Ann. Glaciol. 1, 103112.10.3189/S0260305500017079
Carey, V. P. & Gebhart, B. 1982 Transport near a vertical ice surface melting in a saline water: experiments at low salinities. J. Fluid Mech. 117, 403423.10.1017/S0022112082001682
Cazenave, A. & Llovel, W. 2010 Contemporary sea level rise. Ann. Rev. Mar. Sci. 2 (1), 145173.10.1146/annurev-marine-120308-081105
Cooper, P. & Hunt, G. R. 2010 The ventilated filing box containing a vertically distributed source of buoyancy. J. Fluid Mech. 646, 3958.10.1017/S0022112009992734
Ellison, T. H. & Turner, J. S. 1959 Turbulent entrainment in stratified flows. J. Fluid Mech. 6, 423448.10.1017/S0022112059000738
Galton-Fenzi, B. K., Hunter, J. R., Coleman, R., Marsland, S. J. & Warner, R. C. 2012 Modeling the basal melting and marine ice accretion of the Amery Ice Shelf. J. Geophys. Res. 117, C09031.10.1029/2012JC008214
Gayen, B.2012 Turbulence and internal waves in tidal flow over topography. PhD thesis, ProQuest Dissertations and Theses, Copyright – Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works; Last updated – 2016-03-11.
Gayen, B., Griffiths, R. W. & Hughes, G. O. 2014 Stability transitions and turbulence in horizontal convection. J. Fluid Mech. 751, 698724.10.1017/jfm.2014.302
Gayen, B., Griffiths, R. W. & Kerr, R. C. 2016 Simulation of convection at a vertical ice face dissolving into saline water. J. Fluid Mech. 798, 284298.10.1017/jfm.2016.315
Gayen, B. & Sarkar, S. 2011 Direct and large eddy simulations of internal tide generation at a near critical slope. J. Fluid Mech. 681, 4879.10.1017/jfm.2011.170
George, W. K. & Capp, S. P. 1979 A theory for natural convection turbulent boundary layers next to heated vertical surfaces. Intl J. Heat Mass Transfer 22, 813826.10.1016/0017-9310(79)90021-8
Gladish, C. V., Holland, D. M., Holland, P. R. & Price, S. F. 2012 Ice-shelf basal channels in a coupled ice/ocean model. J. Glaciol. 58, 12271244.10.3189/2012JoG12J003
Grossmann, S. & Lohse, D. 2000 Scaling in thermal convection: a unifying theory. J. Fluid Mech. 407, 2756.10.1017/S0022112099007545
Holland, D. M. & Jenkins, A. J. 1999 Modeling thermodynamic ice–ocean interactions at the base of an ice shelf. J. Phys. Oceanogr. 29, 17871800.10.1175/1520-0485(1999)029<1787:MTIOIA>2.0.CO;2
Holman, J. P. 2010 Heat Transfer (McGraw-Hill Series in Mechanical Engineering), 10th edn. Science Engineering & Math.
Huppert, H. E. & Turner, J. S. 1978 On melting icebergs. Nature 271, 4648.10.1038/271046a0
Huppert, H. E. & Turner, J. S. 1980 Ice blocks melting into a salinity gradient. J. Fluid Mech. 100, 367384.10.1017/S0022112080001206
Husband, W. H. W. & Ozsahin, S. 1967 Rates of dissolution of potash ore. Canad. J. Chem. Engng 45 (4), 234237.10.1002/cjce.5450450410
Jacobs, S. S., Jenkins, A., Giulivi, C. F. & Dutrieux, P. 2011 Stronger ocean circulation and increased melting under Pine Island Glacier ice shelf. Nature Geosci. 4, 519523.10.1038/ngeo1188
, Jenkins, A. 1991 A one-dimensional model of ice shelf–ocean interaction. J. Geophys. Res. 96 (C11), 2067120677.10.1029/91JC01842
Jenkins, A. 2011 Convection-driven melting near the grounding lines of ice shelves and tidewater glaciers. J. Phys. Oceanogr. 41, 22792294.10.1175/JPO-D-11-03.1
Jenkins, A., Dutrieux, P., Jacobs, S. S., 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. Nature Geosci. 3, 468472.10.1038/ngeo890
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, 439473.10.1017/S0022112081002450
Kerr, R. C. 1994 Dissolving driven by vigorous compositional convection. J. Fluid Mech. 280, 287302.10.1017/S0022112094002934
Kerr, R. C. & Mcconnochie, C. D. 2015 Dissolution of a vertical solid surface by turbulent compositional convection. J. Fluid Mech. 765, 211228.10.1017/jfm.2014.722
Lavergne, C., Palter, J. B., Galbraith, E. D., Bernardello, R. & Marinov, I. 2014 Cessation of deep convection in the open Southern Ocean under anthropogenic climate change. Nat. Clim. Change 4, 278282.10.1038/nclimate2132
Magorrian, S. J. & Wells, A. J. 2016 Turbulent plumes from a glacier terminus melting in a stratified ocean. J. Geophys. Res. 121, 46704696.10.1002/2015JC011160
McConnochie, C. D & Kerr, R. C. 2016 The turbulent wall plume from a vertically distributed source of buoyancy. J. Fluid Mech. 787, 237253.10.1017/jfm.2015.691
McConnochie, C. D. & Kerr, R. C. 2016b The effect of a salinity gradient on the dissolution of a vertical ice face. J. Fluid Mech. 791, 589607.10.1017/jfm.2016.62
McConnochie, C. D. & Kerr, R. C. 2017a Enhanced ablation of a vertical ice wall due to an external freshwater plume. J. Fluid Mech. 810, 429447.10.1017/jfm.2016.761
McConnochie, C. D. & Kerr, R. C. 2017b Testing a common ice-ocean parameterization with laboratory experiment. J. Geophys. Res. 122, 59055915.10.1002/2017JC012918
Morgan, V. I. & Budd, W. F. 1978 The distribution, movements and melt rates of Antarctic Iceburghs. In Iceberg Utilization: Proceedings of the First International Conference and Workshops on Iceberg Utilization for Fresh Water Production, Weather Modification and Other Applications Held at Iowa State University, Ames, Iowa, USA, October 2–6, 1977 (ed. Husseiny, A. A.), pp. 220228. Pergamon Press.10.1016/B978-0-08-022916-4.50025-X
Morrison, A. K., Hogg, A. M. & Ward, M. L. 2011 Sensitivity of the Southern Ocean overturning circulation to surface buoyancy forcing. Geophys. Res. Lett. 38, L14602.10.1029/2011GL048031
Morton, B. R., Taylor, G. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. R. Soc. Lond. A 234, 123.
Nilson, R. H. 1985 Countercurrent convection in a double-diffusive boundary layer. J. Fluid Mech. 160, 181210.10.1017/S0022112085003445
Paolo, F. S., Fricker, H. A. & Padman, L. 2016 Constructing improved decadal records of Antarctic ice shelf height change from multiple satellite radar altimeters. Remote Sens. Environ. 177, 192205.10.1016/j.rse.2016.01.026
Payne, A. J., Holland, P. R., Shepherd, A. P., Rutt, I. C., Jenkins, A. & Joughin, I. 2007 Numerical modeling of ocean–ice interaction under Pine Island Bay’s ice shelf. J. Geophys. Res. 112, C10019.10.1029/2006JC003733
Piecuch, C. G & Ponte, R. M. 2014 Mechanisms of global-mean steric sea level change. J. Clim. 27 (2), 824834.10.1175/JCLI-D-13-00373.1
Rignot, E. & Jacobs, S. S. 2002 Rapid bottom melting widespread near Antarctic ice sheet grounding lines. Science 296, 20202023.10.1126/science.1070942
Rydt, J. D. & Gudmundsson, G. H 2016 Coupled ice shelf-ocean modeling and complex grounding line retreat from a seabed ridge. J. Geophys. Res. 121, 865880.
Shepherd, A., Wingham, D. & Rignot, E. 2004 Warm ocean is eroding west antarctic ice sheet. Geophys. Res. Lett. 31 (23), l23402.10.1029/2004GL021106
Slater, D. A., Goldberg, D. N., Nienow, P. W. & Cowton, T. R. 2016 Scalings for submarine melting at tidewater glaciers from buoyant plume theory. J. Phys. Oceanogr. 46 (6), 18391855.10.1175/JPO-D-15-0132.1
Snow, K., Hogg, A. M., Sloyan, B. M. & Downes, S. M. 2016 Sensitivity of Antarctic bottom water to change in surface buoyancy fluxes. J. Clim. 29, 313330.10.1175/JCLI-D-15-0467.1
Spence, P., Griffies, S. M., England, M. H., Hogg, A. M., Saenko, O. A. & Jourdain, N. C. 2014 Rapid subsurface warming and circulation changes of Antarctic coastal waters by poleward shifting winds. Geophys. Res. Lett. 41, 70897096.10.1002/2014GL060613
Swingedouw, D., Fichefet, T., Huybrechts, P., Goosse, H., Driesschaert, E. & Loutre, M. F. 2008 Antarctic ice-sheet melting provides negative feedbacks on future climate warming. Geophys. Res. Lett. 35 (17), 17705.10.1029/2008GL034410
Tsuji, T. & Nagano, Y. 1988 Turbulence measurements in a natural convection boundary layer along a vertical flat plate. Intl J. Heat Mass Transfer 31 (10), 21012111.10.1016/0017-9310(88)90120-2
Turner, J. S. 1979 Buoyancy Effects in Fluids. Cambridge University Press.
Vliet, G. C. & Ross, D. C. 1975 Turbulent natural convection on upward and downward facing inclined constant heat flux surfaces. J. Heat Transfer 97 (4), 549554.10.1115/1.3450427
Washburn, E. W. 1926 International Critical Tables of Numerical Data, Physics, Chemistry and Technology. The National Academies Press.
Weast, R. C., Astle, M. J. & Beyer, W. H. 1989 CRC Handbook of Chemistry and Physics. vol. 1990. CRC Press.
Wells, A. J. & Worster, M. G. 2008 A geophysical-scale model of vertical natural convection boundary layers. J. Fluid Mech. 609, 111137.10.1017/S0022112008002346
Wells, A. J. & Worster, M. G. 2011 Melting and dissolving of a vertical solid surface with laminar compositional convection. J. Fluid Mech. 687, 118140.10.1017/jfm.2011.322
Woods, A. W. 1992 Melting and dissolving. J. Fluid Mech. 239, 429448.10.1017/S0022112092004476
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Ablation of sloping ice faces into polar seawater

  • Mainak Mondal (a1), Bishakhdatta Gayen (a1), Ross W. Griffiths (a1) and Ross C. Kerr (a1)


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