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Inducing predefined nonlinear rogue waves on basis of breather solutions

Authors: Witt, Andy;

Inducing predefined nonlinear rogue waves on basis of breather solutions

Abstract

Der Peregrine Breather, eine analytische Lösung der Nichtlinearen Schroedingergleichung, wird modifiziert, um punkt- und zeitgenau eine zuvor in Form, Höhe und Steilheit definierte nichtlineare Extremwelle in einen beliebigen gerichteten Seegang zu induzieren. Dazu wird zunächst eine Parameterstudie des Störungsterms der instabilen Peregrine Modulation zur Formgebung der Extremwelle durchgeführt. Dabei wird die Phasenmodulation als die entscheidende Störung für die nichtlineare, wachsende Breather-Instabilität identifiziert. Mit diesem Erkenntnisstand wird das Induzieren einer vorbestimmten Extremwelle in nicht uniforme Trägerwellen und sogar irreguläre, gerichtete Seegänge dargestellt, die Grenzen ermittelt und die Dynamiken mittels Phasen- und Spektralanalyse über Zeit und Raum analysiert. Die Ergebnisse werden mit einer realen, auf der Nordsee gemessenen Monsterwelle verglichen und zudem wird sowohl ein Reverse Engineering als auch eine Vorhersagemethode solcher nichtlinearer Extremwellen skizziert.

The Peregrine Breather, an analytical solution of the Nonlinear Schroedinger Equation, is modified to induce locally and temporally accurate, predefined extreme wave events in an arbitrary directed sea state. To this end, a parameter study of the distortion term of the unstable Peregrine modulation is performed to enforce form, height, and steepness of the rogue wave. In addition, the phase modulation is identified to be the crucial perturbation for the nonlinear Breather dynamic. With this knowledge, the inducing of a predefined rogue wave in non-uniform carrier waves and even in irregular, directed sea states is presented, its limits determined, and the Breather dynamics analyzed by spectral and phase evolution analysis in time and space. The results are compared to the dynamics of real occurred extreme waves and a reverse engineering as well as a forecast model for nonlinear real rogue waves are depicted briefly.

Country
Germany
Keywords

reverse engineering, nonlinear Schroedinger equation, nonlinear wave equation, freak wave, water wave, extreme wave, nonlinear waves, forecast model, rogue wave, breather solutions, Technik, Peregrine Breather

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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Average
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