University of Cambridge > > Isaac Newton Institute Seminar Series > Long non-linear flexural-gravitational waves in the sea, covered with Ice

Long non-linear flexural-gravitational waves in the sea, covered with Ice

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SIPW05 - SIP Follow on: Mathematics of sea ice in the twenty-first century

Longwave nonlinear dispersion model, that describes flexural-gravitational waves propagating in icy cover on the surface of the sea, is developed by expanding the original three-dimensional problem of hydroelastic oscillations of the system “elastic plate – a layer of an ideal incompressible fluid of variable depth ” in a small parameter. The model takes into account effects of non-linear fluid dispersion as well inertia, elasticity and geometrically nonlinear plate deflection. Proceeding from received equations, there were built an hierarchical sequence of more simple models, generalizing equations of Peregrine , Boussinesque and Korteweg- de Vries, known from surface waves theories, for the case of flexural-gravitational waves . For the special case of generalized Korteweg-de-Vries equation analitic solutions, describing propagation of solitons and cnoidal waves in the sea, covered with continuous or broken ice, were built and analyzed. It is shown that flexural-gravitational waves possess some mirrored properties as compared to long non-linear water waves. As to soliton this means that without changing the form a depression propagates, not a hump, as in the clean water case, and speed of it’s propagation decreases with increasing the amplitude rather than increases . In addition, the characteristics of the flexural-gravitational waves are determined by the wave amplitude and dispersion of plate flexural rigidity, and do not depend on the water dispersion and inertial properties of the icy cover. There are determined areas of task parameters changing, where various types of soliton-like decisions for given equation may exist. In a similar setting, the generalized Kadomtsev – Petviashvili type equation, modeling the propagation of long non-linear two-dimensional flexural-gravitational waves in the sea covered with continuous ice, has been derived. Assuming periodicity for transverse coordinate, the analitic solution for the equation received has been built in the form of a wave packet. Relations among character parameters of the task , which provide the existence of such a solution, were defined.

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