Numerical modelling of dispersive waves generated by landslide motion. (Russian. English summary) Zbl 1290.76017
Summary: The authors study the surface waves which are generated by the submarine landsliding
on a curvilinear bottom slope of a deep reservoir. The shallow water models of the
first and second approximations are used to describe the surface waves. An underwater
landslide is described by the model of motion of a ”quasi-deformed” body on curvilinear
surface under the effect of mass and external forces. The numerical algorithm for solving
the nonlinear dispersive equations is based on the finite differential approximation of
the hyperbolic system, which is similar to the shallow water equations of the first
hydrodynamic approximation and the elliptic equation for the depth-average dispersive
pressure component. The comparison of the numerical results obtained in the framework of
the dispersion-free shallow water model and the nonlinear dispersive model is done.
MSC:
76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |
76M20 | Finite difference methods applied to problems in fluid mechanics |