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An investigation into the dispersion of ocean surface waves in sea ice

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Abstract

This investigation considers theoretical models and empirical studies related to the dispersion of ocean surface gravity waves propagating in ice covered seas. In theory, wave dispersion is related to the mechanical nature of the ice. The change of normalized wavenumber is shown for four different dispersion models: the mass-loading model, an elastic plate model, an elastic plate model extended to include dissipation, and a viscous-layer model. For each dispersion model, model parameters are varied showing the dependence of deviation from open water dispersion on ice thickness, elasticity, and viscosity. In all cases, the deviation of wavenumber from the open water relation is more pronounced for higher frequencies. The effect of mass loading, a component of all dispersion models, tends to shorten the wavelength. The Voigt model of dissipation in an elastic plate model does not change the wavelength. Elasticity in the elastic plate model and viscosity in the viscous-layer model tend to increase the wavelength. The net effect, lengthening or shortening, is a function of the particular combination of ice parameters and wave frequency. Empirical results were compiled and interpreted in the context of these theoretical models of dispersion. A synopsis of previous measurements is as follows: observations in a loose pancake ice in the marginal ice zone, often, though not always, showed shortened wavelengths. Both lengthening and shortening have been observed in compact pancakes and pancakes in brash ice. Quantitative matches to the flexural-gravity model have been found in Arctic interior pack ice and sheets of fast ice.

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Notes

  1. http://www.apl.washington.edu/project/project.php?id=arctic_sea_state

  2. Also referred to as “added mass” model, the “inertial” model, the “added inertia” model, and possibly others.

  3. Unfamiliar with basic ice types? Please see http://seaiceatlas.snap.uaf.edu/glossary for detailed definitions. Ice types mentioned in this manuscript are pancake, frazil, brash, grease, pack ice, and fast ice sheets.

  4. In the literature, the imaginary part of the complex wavenumber is also denoted as k i or q

  5. In Mosig et al. [2015], this is called viscosity parameter, but here, we use dissipation to avoid confusion with viscous-layer model introduced in the following section. The symbol η is not to be confused with sea surface elevation.

  6. A reviewer pointed out that an asymptotic expansion in the dissipation parameter should be possible.

  7. However, Fox and Haskell [2001] did not make this connection: “While the added-mass and ice-sheet models predict dispersion equations with power laws less than 2, we found that the measured dispersion equation has a power law with exponent greater than 2.” Referring to either the statement or the result, Squire said it was “perplexing” in his 2007 review paper.

  8. For the cases of shortening, this implies even a stronger change in dispersion than measured, and for the cases of lengthening this implies a lesser change in dispersion (or none at all).

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Acknowledgements

COC was supported by an ASEE postdoctoral fellowship and a Karles fellowship at NRL. Discussions with A. Marchenko (University Center in Svalbard), A. Babanin (University of Melbourne), and a presentation by W. Perrie (Bedford Institute of Oceanography) motivated this paper. The comments of J. Mosig and V. Squire (University of Otago) greatly improved an early version of this manuscript. We are additionally grateful to V. Squire who supplied a code for the EFS model. We also acknowledge clarifying discussions with P. Wadhams (Cambridge University) and H. Shen (Clarkson University). We thank Editor O. Breivik and the two anonymous reviewers for their diligence and patience through multiple revisions which lead to a substantially improved manuscript.

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  1. US Naval Research Laboratory, Oceanography Division, 1005 Balch Blvd, Stennis Space Center, Hancock County, MS, 39529, USA

    Clarence Olin Collins III & William Erick Rogers

  2. Department of Ocean Sciences, University of Miami, Rosenstiel School of Marine and Atmospheric Science, Miami, FL, USA

    Björn Lund

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  1. Clarence Olin Collins III
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Correspondence to Clarence Olin Collins III.

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Responsible Editor: Oyvind Breivik

This article is part of the Topical Collection on the 14th International Workshop on Wave Hindcasting and Forecasting in Key West, Florida, USA, November 8–13, 2015

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Collins, C.O., Rogers, W.E. & Lund, B. An investigation into the dispersion of ocean surface waves in sea ice. Ocean Dynamics 67, 263–280 (2017). https://doi.org/10.1007/s10236-016-1021-4

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