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Wave patterns beneath an ice cover

Presented by: 
Andrej Il’ichev Steklov Mathematical Institute, Russian Academy of Sciences
Tuesday 3rd October 2017 - 16:15 to 17:00
INI Seminar Room 1
We prove existence of the soliton-like solutions of the full system of equations which describe wave propagation in the fluid of a finite depth under an ice cover. These solutions correspond to solitary waves of various nature propagating along the water-ice interface. We consider the plane-parallel movement in a layer of the perfect fluid of the finite depth which characteristics obey the full 2D Euler system of equations. The ice cover is modeled by the elastic Kirchgoff-Love plate and it has a considerable thickness so that the plate inertia is taken into consideration when the model is formulated. The Euler equations contain the additional pressure arising from the presence of the elastic plate freely floating on the liquid surface. The mentioned families of the solitary waves are parameterized by a speed of the wave and their existence is proved for the speeds lying in some neighborhood of its critical value corresponding to the quiescent state. S olitary waves, in their turn, bifurcate from the quiescent state and lie in some neighborhood of it. By other words, existence of solitary waves of sufficiently small amplitudes on the water-ice interface is proved. The proof is conducted with the help of the projection of the required system to the central manifold and further analysis of the resulting reduced finite dimensional dynamical system on the central manifold.
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