Super rogue waves in simulations based on weakly nonlinear and fully nonlinear hydrodynamic equations

Journal
Physical review E - Covering statistical, nonlinear, biological, and soft matter physics  
Volume
88
Issue
1
Article Number
012909
Citation
Physical review E 88 (1): 012909 (2012)
Publisher DOI
10.1103/PhysRevE.88.012909
Scopus ID
2-s2.0-84880580338
ArXiv ID
1212.6619v2
Publisher
The American Physical Society
The rogue wave solutions (rational multi-breathers) of the nonlinear Schrodinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation (MNLS) also known as the Dysthe equation. This numerical modelling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub2012c. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.
Subjects
Physics - Fluid Dynamics
Physics - Fluid Dynamics
Physics - Geophysics
DDC Class
530: Physik
550: Geowissenschaften