V.O.Tkachenko, V.V.Yakovlev Nonlinear-dispersion models of the surface waves in sea coated by ice |
Applied hydromechanics, Vol. 1 (73) ¹ 3, (1999) |
| The long-wave nonlinear-dispersion model,describing propagation of bending-gravitational waves in a elastic plate, floating on a surface of variable depth liquid is constracted. The model takes in to account effects of nonlinear dispersion and inertion, elasticity and geometrical nonlinear deflection of plates. On the basis of the general model the hierarchical sequence of more simple models is developed. This models generalize the known in the water wave theory the models of Peregreen, Boussinesq and Korteweg - de Vrise on the case of the flexural-gravitational waves. In particular case of generalized equation of Korteweg - de Vrise a exact solution has been obtained. This solution discribes the properties of solitons and cnoidal waves in the sea covered broken and unbroken ice. It is shown that the flexural-gravitational waves are over furned, in comparison with the long nonlinear water waves. With regard to the solitons it means, that without change of the form surface propagatio the trough, while in the water propagation the crest. The velocity propagation of flexural - gravitational waves with increase of amplitude decreases. Moreover the characteristics the flexural gravitational waves are determined by amplitude and dispersion of flexural rigidity of a plate and do not depend on water dispersion and inertial properties of ice cover. |
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| TEXT LANGUAGE: Russian |