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Wave Propagation in Viscoelastic Materials over Water

Presented by: 
Hayley Shen
Tuesday 3rd October 2017 - 14:15 to 15:00
INI Seminar Room 1
Ice covers over water modify the mass, energy, and momentum transfer between the atmosphere and ocean. Ocean wave propagation is one of the numerous topics from these three basic processes. Because of the Arctic ice reduction, longer fetch has increased both the intensity and the dominant wave period. Longer period waves damp much less. They thus propagate further into ice covers. The contemporary Arctic system cannot be properly evaluated without a good grasp of the growing presence of waves under ice covers. Ice covers are complex materials. Even a continuous solid ice cover does not fit into a simple constitutive model. In the field ice covers often are consisted of discontinuous pieces of various sizes and shapes, mixed with open water or slurry of ice crystals. Such a composite cover has been idealized as a linear viscoelastic material. This hypothesis is based on a simple physical argument: all materials under deformation simultaneously store some and dissipate some energy. The first order approximation is therefore a linear viscoelastic model. To test this hypothesis, the dominant characteristics of the model must be thoroughly understood. The most important characteristic of wave propagation is the dispersion relation. Even with a simple linear viscoelastic model, the dispersion relation is complicated. There are many roots all satisfy the dispersion relation. All of them may be present under different conditions. In this talk, a description of these roots and their physical meanings will be presented. Their presence has been found in other fields. Knowledge from other fields may shed light on how these different wave modes interact under different situations. 
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons