On the nonlinear Schr\"odinger equation for waves on a nonuniform current
Fluid Dynamics
2017-04-14 v1 Atmospheric and Oceanic Physics
Abstract
A nonlinear Schr\"odinger equation with variable coefficients for surface waves on a large-scale steady nonuniform current has been derived without the assumption of a relative smallness of the velocity of the current. This equation can describe with good accuracy the loss of modulation stability of a wave coming to a counter current, leading to the formation of so called rogue waves. Some theoretical estimates are compared to the numerical simulation with the exact equations for a two-dimensional potential motion of an ideal fluid with a free boundary over a nonuniform bottom at a nonzero average horizontal velocity.
Cite
@article{arxiv.1704.04016,
title = {On the nonlinear Schr\"odinger equation for waves on a nonuniform current},
author = {V. P. Ruban},
journal= {arXiv preprint arXiv:1704.04016},
year = {2017}
}
Comments
6 pages, 10 figures, published in 2012