This thesis investigates the effect of viscous damping on rogue wave formation and permanent downshift using the higher-order nonlinear Schrödinger equation (HONLS). The strength of viscous damping is varied and compared to experiments with only linear damped HONLS.
Stability analysis of the linear damped HONLS equation shows that instability stabilizes over time. This analysis also provides an instability criterion in the case of HONLS with viscous damping.
Numerical experiments are conducted in the two unstable mode regime using perturbations of the Stokes wave as initial data. With only linear damping permanent downshift is not observed and rogue wave formation is decreased. The addition of viscous damping leads to permanent downshift and a slight increase in rogue wave activity. Analysis of the energy and momentum gives a possible explanation for this behavior.
Schober, Constance M.
Bachelor of Science (B.S.)
College of Sciences
Length of Campus-only Access
Smith, Evelyn, "The Effects of Viscous Damping on Rogue Wave Formation and Permanent Downshift in the Nonlinear Schrödinger Equation" (2022). Honors Undergraduate Theses. 1211.