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Master
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Fourth-Order Nonlinear Schrödinger Equation as a Model for Water Waves Envelope Propagation in Intermediate Depth

Master program titleMaster de physique
Defense date2021-09-07
Abstract

In this work we develop nonlinear models to study the propagation of surface water waves.The Nonlinear Schrödinger Equation (NLSE) is used to describe the evolution of the envelope of a wave packet. However, the NLSE, an equation obtained at third order in steepness in the multiscale expansion, is symmetric in time. Therefore it is unable to reproduce the asymmetric development of the water waves envelope. We then propose four models obtained at fourth order in steepness to recover asymmetry and improve the agreement with experiments. Those four models are adapted from the fourth-order NLSE found in the literature. With those models, we perform numerical simulations of the envelope propagation in space. We simulate the water waves as propagating in one direction along a wave tank of constant depth. This simulation is performed with the third-order NLSE and the four fourth-order models for different physical parameters (water depth, carrier wave frequency, steepness of the wave). We then study the impact of the modified fourth-order models on the envelope propagation and we carefully investigate the role of each term in such model equations. On the other hand we compare our simulations with real measurement in the wave flume of the University of Sydney. We then analyse the agreement between our models and the experiment.

eng
Keywords
  • Rogue wave
  • Vague scélérate
  • NLSE
  • Equation de Schrödinger non-linéaire
  • Nonlinear Schrödinger equation
  • Nonlinear propagation
  • Propagation non-linéaire
Citation (ISO format)
MONTESSUIT, Corentin Pierre Gabriel. Fourth-Order Nonlinear Schrödinger Equation as a Model for Water Waves Envelope Propagation in Intermediate Depth. 2021.
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Master thesis
accessLevelRestricted
Identifiers
  • PID : unige:155452
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Technical informations

Creation10/13/2021 1:21:00 PM
First validation10/13/2021 1:21:00 PM
Update time03/16/2023 1:31:27 AM
Status update03/16/2023 1:31:26 AM
Last indexation01/29/2024 10:48:25 PM
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