The Effects Of Wind And Nonlinear Damping On Rogue Waves And Permanent Downshift

Keywords

Downshifting; Freak wave; Nonlinear damping; Nonlinear Schrödinger equation; Rogue wave; Wind action

Abstract

In this paper we investigate the effects of wind and nonlinear damping on permanent downshift and the formation of rogue waves in the framework of a HONLS model. Wind effects are incorporated by including a uniform linear damping/forcing term in the model. The strength of the wind, Γ, is allowed to vary as well as wind duration. Determining permanent downshift is not straightforward and we propose a criteria for permanent downshift related to our numerical experiments. We consider large ensembles of initial data for modulated unstable Stokes waves with N=1,2,3 unstable modes. In the nonlinear damped HONLS evolution we find that permanent downshift is observed whenever the strength of the nonlinear damping β>0.1. Notably, rogue waves typically do not develop after the time of permanent downshift, implying that a downshifted sea-state does not allow for any further rogue waves. Incorporating wind effects into the nonlinear damped HONLS model, we find that damping by the wind weakens downshifting while forcing by the wind enhances downshifting. The proximity of the initial data to unstable plane waves impacts the characteristic features of the rogue waves in the nonlinear damped HONLS evolution. We find that as the initial data is chosen closer to the plane wave, the maximum strength, number, and lifetime of rogue waves increase while the time of permanent downshift decreases. Alternatively, we show that the greater the wave strength, the more rogue waves, or the longer their lifetime, the earlier permanent downshift occurs.

Publication Date

12-1-2015

Publication Title

Physica D: Nonlinear Phenomena

Volume

313

Number of Pages

81-98

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.physd.2015.09.010

Socpus ID

84944899227 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84944899227

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