Hostname: page-component-8448b6f56d-sxzjt Total loading time: 0 Render date: 2024-04-19T13:51:12.763Z Has data issue: false hasContentIssue false

Ice scallops: a laboratory investigation of the ice–water interface

Published online by Cambridge University Press:  28 June 2019

Mitchell Bushuk*
Geophysical Fluid Dynamics Laboratory, NOAA, Princeton, NJ 08540, USA Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
David M. Holland
Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA Center for Global Sea Level Change, New York University Abu Dhabi, P.O. 129188, UAE
Timothy P. Stanton
Department of Oceanography, Naval Postgraduate School, Monterey, CA 93943, USA
Alon Stern
Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Callum Gray
LaVision Inc., Ypsilanti, MI 48197, USA
Email address for correspondence:


Ice scallops are a small-scale (5–20 cm) quasi-periodic ripple pattern that occurs at the ice–water interface. Previous work has suggested that scallops form due to a self-reinforcing interaction between an evolving ice-surface geometry, an adjacent turbulent flow field and the resulting differential melt rates that occur along the interface. In this study, we perform a series of laboratory experiments in a refrigerated flume to quantitatively investigate the mechanisms of scallop formation and evolution in high resolution. Using particle image velocimetry, we probe an evolving ice–water boundary layer at sub-millimetre scales and 15 Hz frequency. Our data reveal three distinct regimes of ice–water interface evolution: a transition from flat to scalloped ice; an equilibrium scallop geometry; and an adjusting scallop interface. We find that scalloped-ice geometry produces a clear modification to the ice–water boundary layer, characterized by a time-mean recirculating eddy feature that forms in the scallop trough. Our primary finding is that scallops form due to a self-reinforcing feedback between the ice-interface geometry and shear production of turbulent kinetic energy in the flow interior. The length of this shear production zone is therefore hypothesized to set the scallop wavelength.

JFM Papers
© 2019 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.)


Achenbach, E. 1974 The effects of surface roughness and tunnel blockage on the flow past spheres. J. Fluid Mech. 65 (1), 113125.Google Scholar
Adrian, R. J. 2005 Twenty years of particle image velocimetry. Exp. Fluids 39 (2), 159169.Google Scholar
Adrian, R. J. & Westerweel, J. 2011 Particle Image Velocimetry. Cambridge University Press.Google Scholar
Ashton, G. D. 1972 Turbulent heat transfer to wavy boundaries. In Proceedings of the 1972 Heat Transfer Fluid Mech. Inst., pp. 200213. Stanford University Press.Google Scholar
Ashton, G. D. & Kennedy, J. F. 1972 Ripples on underside of river ice covers. J. Hydraulics Division 98 (9), 16031624.Google Scholar
Blumberg, P. N. & Curl, R. L. 1974 Experimental and theoretical studies of dissolution roughness. J. Fluid Mech. 65 (4), 735751.Google Scholar
Camporeale, C. & Ridolfi, L. 2012 Ice ripple formation at large Reynolds numbers. J. Fluid Mech. 694, 225251.Google Scholar
Carey, K. L. 1966 Observed configuration and computed roughness of the underside of river ice, St Croix River, Wisconsin. US Geol. Survey Prof. Paper Paper 550, B192B198.Google Scholar
Claudin, P., Durán, O. & Andreotti, B. 2017 Dissolution instability and roughening transition. J. Fluid Mech. 832, R2.Google Scholar
Curl, R. L. 1966 Scallops and flutes. Trans. Cave Res. Group 7, 121160.Google Scholar
Dansereau, V., Heimbach, P. & Losch, M. 2014 Simulation of subice shelf melt rates in a general circulation model: velocity-dependent transfer and the role of friction. J. Geophys. Res.: Oceans 119 (3), 17651790.Google Scholar
Emery, W. J. & Thomson, R. E. 2001 Data Analysis Methods in Physical Oceanography, vol. 59, p. 180. Elsevier Science.Google Scholar
Feltham, D. L., Worster, M. G. & Wettlaufer, J. S. 2002 The influence of ocean flow on newly forming sea ice. J. Geophys. Res.: Oceans 107 (C2), 19.Google Scholar
Gilpin, R. R., Hirata, T. & Cheng, K. C. 1980 Wave formation and heat transfer at an ice–water interface in the presence of a turbulent flow. J. Fluid Mech. 99, 619640.Google Scholar
Goto, Y., Yasuda, I. & Nagasawa, M. 2016 Turbulence estimation using fast-response thermistors attached to a free-fall vertical microstructure profiler. J. Atmos. Ocean. Technol. 33 (10), 20652078.Google Scholar
Hanratty, T. J. 1981 Stability of surfaces that are dissolving or being formed by convective diffusion. Annu. Rev. Fluid Mech. 13 (1), 231252.Google Scholar
Hellmer, H. H. & Olbers, D. J. 1989 A two-dimensional model for the thermohaline circulation under an ice shelf. Antarctic Sci. 1 (4), 325336.Google Scholar
Hobson, B. W., Sherman, A. D. & McGill, P. R. 2011 Imaging and sampling beneath free-drifting icebergs with a remotely operated vehicle. Deep-Sea Res. II 58 (11-12), 13111317.Google Scholar
Holland, D. M. & Jenkins, A. 1999 Modeling thermodynamic ice–ocean interactions at the base of an ice shelf. J. Phys. Oceanogr. 29 (8), 17871800.Google Scholar
Hsu, K.-S., Locher, F. A. & Kennedy, J. F. 1979 Forced-convection heat transfer from irregular melting wavy boundaries. Trans. ASME J. Heat Transfer 101 (4), 598602.Google Scholar
Jenkins, A. 1991 A one-dimensional model of ice shelf-ocean interaction. J. Geophys. Res.: Oceans 96 (C11), 2067120677.Google Scholar
Jenkins, A., Nicholls, K. W. & Corr, H. F. J. 2010 Observation and parameterization of ablation at the base of Ronne Ice Shelf, Antarctica. J. Phys. Oceanogr. 40 (10), 22982312.Google Scholar
Kader, B. A. & Yaglom, A. M. 1972 Heat and mass transfer laws for fully turbulent wall flows. Intl J. Heat Mass Transfer 15 (12), 23292351.Google Scholar
McPhee, M. 2008 Air–Ice–Ocean Interaction: Turbulent Ocean Boundary Layer Exchange Processes. Springer.Google Scholar
McPhee, M. G. 1992 Turbulent heat flux in the upper ocean under sea ice. J. Geophys. Res.: Oceans 97 (C4), 53655379.Google Scholar
McPhee, M. G., Maykut, G. A. & Morison, J. H. 1987 Dynamics and thermodynamics of the ice/upper ocean system in the marginal ice zone of the Greenland Sea. J. Geophys. Res.: Oceans 92 (C7), 70177031.Google Scholar
Mellor, G. L., McPhee, M. G. & Steele, M. 1986 Ice–seawater turbulent boundary layer interaction with melting or freezing. J. Phys. Oceanogr. 16 (11), 18291846.Google Scholar
Nelson, J. M., McLean, S. R. & Wolfe, S. R. 1993 Mean flow and turbulence fields over two-dimensional bed forms. Water Resour. Res. 29 (12), 39353953.Google Scholar
Pedocchi, F., Martin, J. E. & García, M. H. 2008 Inexpensive fluorescent particles for large-scale experiments using particle image velocimetry. Exp. Fluids 45 (1), 183186.Google Scholar
Ramudu, E., Hirsh, B. H., Olson, P. & Gnanadesikan, A. 2016 Turbulent heat exchange between water and ice at an evolving ice–water interface. J. Fluid Mech. 798, 572597.Google Scholar
Richmond, P. W. & Lunardini, V. J.1990 Heat transfer from water flowing through a chilled-bed open channel. Tech. Rep. DTIC Document.Google Scholar
Schlichting, H., Gersten, K., Krause, E., Oertel, H. & Mayes, K. 1960 Boundary-Layer Theory, vol. 7. Springer.Google Scholar
Seki, N., Fukusako, S. & Younan, G. W. 1984 Ice-formation phenomena for water flow between two cooled parallel plates. Trans. ASME J. Heat Transfer 106 (3), 498505.Google Scholar
Stanton, T. P.2001 A turbulence-resolving coherent acoustic sediment flux probe device and method for using. US Patent 6,262,942.Google Scholar
Steele, M., Mellor, G. L. & McPhee, M. G. 1989 Role of the molecular sublayer in the melting or freezing of sea ice. J. Phys. Oceanogr. 19 (1), 139147.Google Scholar
Stefan, J. 1891 On the theory of ice formation, especially ice formation in the polar seas. Ann. Phys. 278 (2), 269286.Google Scholar
Thomas, R. M. 1979 Size of scallops and ripples formed by flowing water. Nature 277 (5694), 281.Google Scholar
Thorsness, C. B. & Hanratty, T. J. 1979a Mass transfer between a flowing fluid and a solid wavy surface. AIChE J. 25 (4), 686697.Google Scholar
Thorsness, C. B. & Hanratty, T. J. 1979b Stability of dissolving or depositing surfaces. AIChE J. 25 (4), 697701.Google Scholar
Wettlaufer, J. S. 1991 Heat flux at the ice–ocean interface. J. Geophys. Res.: Oceans 96 (C4), 72157236.Google Scholar
Wieneke, B. 2015 PIV uncertainty quantification from correlation statistics. Meas. Sci. Technol. 26 (7), 074002.Google Scholar
Willert, C. E. & Gharib, M. 1991 Digital particle image velocimetry. Exp. Fluids 10 (4), 181193.Google Scholar
Wykes, M. S. D., Mac Huang, J., Hajjar, G. A. & Ristroph, L. 2018 Self-sculpting of a dissolvable body due to gravitational convection. Phys. Rev. Fluids 3 (4), 043801.Google Scholar
Supplementary material: PDF

Bushuk et al. supplementary material

Bushuk et al. supplementary material 1

Download Bushuk et al. supplementary material(PDF)