Recent developments in applied mathematics and mechanics: theory, experiment and practice. Devoted to the 80th anniversary of academician N.N.Yanenko

Akademgorodok, Novosibirsk, Russia, June 24 - 29, 2001

Abstracts

Novosibirsk participants

Progressing surface waves over an underwater ridge

Kuznetsov D.

Lavrentiev Institute of Hydrodymamics of the Siberian Division of Russian Academy of Sciences (Novosibirsk)

The problem of the wave-guide of surface gravitational waves is investigated since 1950-s. That time M.A.Lavrentiev suggested that hydrodynamics equations allow solutions, describing a wave-guide character of perturbation distributions.

In 60-s and 70-s R.M.Garipov, E.I.Bichenkov, V.I.Nalimov, P.I.Plotnikov were investigated analytically the problem of surface gravitational waves over the underwater ridge. Their investigations were based on the linear theory and non-linear approximation of the long-wave theory. It was shown that underwater ridges can be wave-guides for surface gravitational waves. The asymptotic form (for a large time) of the wave amplitude was found.

In the present work the problem of a progressing small-amplitude waves over underwater ridge is studied in the context of the exact non-linear model of the ideal water. A liquid is suggested to be incompressible and non-vortical.

The theorem of existence of the Euler-equations solutions is proved in the classes of functions, periodical in the direction of the ridge and exponentially fading in the perpendicular to the ridge direction.

Note. Abstracts are published in author's edition

Comments

[Home]
[Conference]