English

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.

Keywords

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

R2 v1 2026-06-22T19:16:25.290Z