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International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Imprimir: 2152-5102
ISSN En Línea: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v28.i1-2.100
pages 135-150

Nonlinear-Dispersive Model of Surface Wave Transformation in Littoral Zone of Sea Covered With Ice

V. O. Tkachenko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
V. V. Yakovlev
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine


The long-wave nonlinear-dispersion model, describing the propagation of flexural-gravitational waves in an elastic plate, floating on a surface of a liquid of variable depth, is constructed. The model takes into account effects of the 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 models of Peregreen, Boussinesq and Korteweg - de Vries for the case of the flexural-gravitational waves. In the particular case of generalized equation of Korteweg - de Vries an exact solution has been obtained. This solution describes the properties of solitons and cnoidal waves in the sea covered with the broken and unbroken ice. It is shown that the flexural-gravitational waves are overturned, in comparison with the long nonlinear water waves. With regard to the solitons it means, that the trough propagates without changes of the surface form, while for the clear water the crest does. The propagation velocity of flexural-gravitational waves decreases with the increase of wave amplitude. Moreover the characteristics of flexural gravitational waves are determined by the wave amplitude and dispersion due to flexural rigidity of the plate and do not depend on water dispersion and inertial properties of the ice cover.