Hamiltonian formulation of the stochastic surface wave problem - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Year : 2022

Hamiltonian formulation of the stochastic surface wave problem

Abstract

We devise a stochastic Hamiltonian formulation of the water wave problem. This stochastic representation is built within the framework of the modelling under location uncertainty. Starting from restriction to the free surface of the general stochastic fluid motion equations, we show how one can naturally deduce Hamiltonian structure under a small noise assumption. Moreover, as in the classical water wave theory, the non-local Dirichlet-Neumann operator appears explicitly in the energy functional. This, in particular, allows us, in the same way as in deterministic setting, to conduct systematic approximations of the Dirichlet-Neumann operator and to infer di↵erent simplified wave models including noise in a natural way.
Fichier principal
Vignette du fichier
Dinvay-Memin-Proc-Roy-Soc-22.pdf (1.25 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03777888 , version 1 (15-09-2022)

Identifiers

Cite

Evgueni Dinvay, Etienne Mémin. Hamiltonian formulation of the stochastic surface wave problem. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2022, pp.1-26. ⟨10.1098/rspa.2022.0050⟩. ⟨hal-03777888⟩
30 View
28 Download

Altmetric

Share

Gmail Facebook X LinkedIn More