"Numerical simulation of Freak Waves"
A. Dyachenko (ITP RAS)
Abstract:
Modulation
instability as the main mechanism of formation of waves of large amplitude
- freak waves - at the surface of deep ocean is considered. Numerical
simulation of nonlinear stage of modulation instability is presented.
Simulation is done using two-dimensional code, based on conformal mapping
of the fluid to the lower half-plane. We have observed that freak
wave has the same ratio of the wave height to the wave length as for the
limiting Stokes wave. When freak wave reaches this limiting state, it
breaks. Numerical simulation of potential flows with a free surface of
two-dimensional fluid is based on combination of the conformal
mapping and Hamiltonian formalism. Method is efficient for study of
strongly nonlinear effects in hydrodynamics of gravity waves.