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The Cryosphere An interactive open-access journal of the European Geosciences Union
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© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 08 Jul 2019

Submitted as: research article | 08 Jul 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal The Cryosphere (TC).

Wave energy attenuation in fields of colliding ice floes. Part A: Discrete-element modelling of dissipation due to ice–water drag

Agnieszka Herman1, Sukun Cheng2, and Hayley H. Shen3 Agnieszka Herman et al.
  • 1Institute of Oceanography, University of Gdansk, Poland
  • 2Nansen Environmental and Remote Sensing Center, Bergen, Norway
  • 3Department of Civil and Environmental Engineering, Clarkson University, Potsdam, NY, USA

Abstract. The energy of water waves propagating through sea ice is attenuated due to nondissipative (scattering) and dissipative processes. The nature of those processes and their contribution to attenuation depends on wave characteristics and ice properties, and is usually difficult (or impossible) to determine from limited observations available. Therefore, many aspects of relevant dissipation mechanisms remain poorly understood. In this work, a discrete-element model (DEM) is used to study one of those mechanisms: dissipation due to ice-water drag. The model consists of two coupled parts, a DEM simulating the surge motion and collisions of ice floes driven by waves, and a wave module solving the wave energy transport equation with source terms computed based on phase-averaged DEM results. The wave energy attenuation is analyzed analytically for a limiting case of a compact, horizontally confined ice cover. It is shown that the usage of a quadratic drag law leads to nonexponential attenuation of wave amplitude a with distance x, of a form a(x)=1/(α x+1/a0), with the attenuation rate α linearly proportional to the drag coefficient. The dependence of α on wave frequency ω varies with the dispersion relation used: for the open-water (ow) dispersion relation, α~ω4; for mass-loading dispersion relation, suitable for ice covers composed of small floes, the increase of α with ω is much faster than in the ow case, leading to very fast elimination of high-frequency components from the wave energy spectrum; for elastic-plate dispersion relation, suitable for large floes or continuous ice, α~ωm within the high-frequency tail, with m close to 2.0–2.5, i.e., dissipation is much slower than in the ow case. The coupled DEM-wave model predicts the existence of two zones: a relatively narrow area of very strong attenuation close to the ice edge, with energetic floe collisions and therefore high instantaneous ice-water velocities; and an inner zone where ice floes are in (semi)permanent contact with each other, with attenuation rates close to those analyzed theoretically. Dissipation in the collisional zone increases with increasing restitution coefficient of the ice and with decreasing floe size. In effect, two factors contribute to strong attenuation in fields of small ice floes: lower wave energy propagation speeds and higher relative ice--water velocities due to larger accelerations of floes with smaller mass and more collisions per unit surface area.

Agnieszka Herman et al.
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Agnieszka Herman et al.
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Publications Copernicus
Short summary
Sea ice interactions with waves are extensively studied in recent years, but mechanisms leading to wave energy attenuation in sea ice remain poorly understood. Close to the ice edge, processes contributing to dissipation include collisions between ice floes and turbulence generated under the ice due to velocity differences between ice and water. This paper analyzes details of those processes both theoretically and by means of a numerical model.
Sea ice interactions with waves are extensively studied in recent years, but mechanisms leading...