Affiliation:
1. Department of Mathematics College of Charleston Charleston South Carolina USA
2. Department of Mathematics Wake Forest University Winston‐Salem North Carolina USA
3. Department of Mathematics University of Central Florida Orlando Florida USA
Abstract
AbstractWe investigate a higher order nonlinear Schrödinger equation with linear damping and weak viscosity, recently proposed as a model for deep water waves exhibiting frequency downshifting. Through analysis and numerical simulations, we discuss how the viscosity affects the linear stability of the Stokes wave solution, enhances rogue wave formation, and leads to permanent downshift in the spectral peak. The novel results in this work include the analysis of the transition from the initial Benjamin–Feir instability to a predominantly oscillatory behavior, which takes place in a time interval when most rogue wave activity occurs. In addition, we propose new criteria for downshifting in the spectral peak and determine the relation between the time of permanent downshift and the location of the global minimum of the momentum and the magnitude of its second derivative.
Funder
Simons Foundation
Engineering and Physical Sciences Research Council
College of Charleston
University of Central Florida
Isaac Newton Institute for Mathematical Sciences