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Effective Rheology and Wave Propagation in the Marginal Ice Zone

Presented by: 
Christian Samspon University of Utah, University of Utah, UNC Chapel Hill and RIMS
Tuesday 12th September 2017 - 14:30 to 15:00
INI Seminar Room 1
Co-authors: Ken Golden (University of Utah), Ben Murphy (University of Utah), Elena Cherkaev (University of Utah)

Wave-ice interactions in the polar oceans comprise a complex but important set of processes influencing sea ice extent, ice pack albedo, and ice thickness. In both the Arctic and Antarctic, the ice floe size distribution in the Marginal Ice Zone (MIZ) plays a central role in the properties of wave propagation. Ocean waves break up and shape the ice floes which, in turn, attenuate various wave characteristics. Recently, continuum models have been developed which treat the MIZ as a two-component composite of ice and slushy water. The top layer has been taken to be purely elastic, purely viscous or viscoelastic. At the heart of these models are effective parameters, namely, the effective elasticity, viscosity, and complex viscoelasticity. In practice, these effective parameters, which depend on the composite geometry and the physical properties of the constituents, are quite difficult to determine. To help overcome this limitation, we employ the methods of homogenization theory, in a quasistatic, fixed frequency regime, to find a Stieltjes integral representation for the complex viscoelasticity.
This integral representation involves the spectral measure of a self adjoint operator and provides what we believe are the first rigorous bounds on the effective viscoelasticity of the sea ice pack. The bounds themselves depend on the moments of the measure which in turn depend on the geometry of the ice floe configurations. This work has the potential to provide simple parameterizations of wave properties which take into account floe concentration and geometry.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons