2022/01/19 by Evgueni Dinvay, Dinvay, Evgueni, Étienne Mémin +1
Earth and Planetary Sciences · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Ocean Waves and Remote Sensing
paper · pdf · doi:10.48550/arxiv.2201.07764
openalex publication_date 2022/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 different simplified wave models including noise in a natural way.