We study statistical properties after a sudden episode of wind for water waves propagating in one direction. A wave with random initial conditions is propagated using a forced-damped higher order Nonlinear Schrödinger equation (NLS). During the wind episode, the wave action increases, the spectrum broadens, the spectral mean shifts up and the Benjamin-Feir index (BFI) and the kurtosis increase. Conversely, after the wind episode, the opposite occurs for each quantity. The kurtosis of the wave height distribution is considered the main parameter that can indicate whether rogue waves are likely to occur in a sea state, and the BFI is often mentioned as a means to predict the kurtosis. However, we find that while there is indeed a quadratic relation between these two, this relationship is dependent on the details of the forcing and damping. Instead, a simple and robust quadratic relation does exist between the kurtosis and the bandwidth. This could allow for a single-spectrum assessment of the likelihood of rogue waves in a given sea state. In addition, as the kurtosis depends strongly on the damping and forcing coefficients, by combining the bandwidth measurement with the damping coefficient, the evolution of the kurtosis after the wind episode can be predicted.
Macro-micro decomposition for consistent and conservative model order reduction of hyperbolic shallow water moment equations: A study using POD-Galerkin and dynamical low rank approximation
The Riemann problem for the shallow water equations with discontinuous topography
Laboratoire Jacques-Louis Lions & Centre National de la Recherche Scientifique, Université de Paris 6（雅克-路易·利翁斯实验室与法国国家科学研究中心，巴黎第六大学）；Department of Mathematics, International University（国际大学数学系）
Effect of directionality on extreme wave formation during nonlinear shoaling
Harbin Engineering University（哈尔滨工程大学）；Dalian University of Technology（大连理工大学）；National Marine Environmental Monitoring Center（国家海洋环境监测中心）；EDF R&D（法国电力集团研发中心）；Laboratoire National d’Hydraulique et Environnement (LNHE)（国家水力学与环境实验室）；LHSV, ENPC, Institut Polytechnique de Paris（巴黎理工学院ENPC LHSV）；Nanyang Technological University（南洋理工大学）
