A comparative study of bi-directional Whitham systems
Résumé
In 1967, Whitham proposed a simplified surface water-wave model which combined the full linear dispersion relation of the full Euler equations with a weakly linear approximation. The equation he postulated which is now called the Whitham equation has recently been extended to a system of equations allowing for bi-directional propagation of surface waves. A number of different two-way systems have been put forward, and even though they are similar from a modeling point of view, these systems have very different mathematical properties. In the current work, we review some of the existing fully dispersive systems. We use state-of-the-art numerical tools to try to understand existence and stability of solutions to the initial-value problem associated to these systems. We also put forward a new system which is Hamiltonian and semi-linear. The new system is shown to perform well both with regard to approximating the full Euler system, and with regard to well posedness properties.
Domaines
Mécanique des fluides [physics.class-ph] Dynamique des Fluides [physics.flu-dyn] Equations aux dérivées partielles [math.AP] Analyse numérique [math.NA] Physique mathématique [math-ph] Analyse classique [math.CA] Systèmes Solubles et Intégrables [nlin.SI] Formation de Structures et Solitons [nlin.PS] Physique mathématique [math-ph] Physique Atmosphérique et Océanique [physics.ao-ph] Physique Numérique [physics.comp-ph] Physique Classique [physics.class-ph] Physique Générale [physics.gen-ph] Géophysique [physics.geo-ph]| Origine | Fichiers produits par l'(les) auteur(s) |
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