Hamiltonian formulation of the stochastic surface wave problem

We devise a stochastic Hamiltonian formulation of the water wave problem. This representation is built within framework modelling under location uncertainty. Starting from restriction to free surface general fluid motion equations, we show how one can naturally deduce structure small noise assumption. Moreover, as in classical theory, non-local Dirichlet–Neumann operator appears explicitly energy functional. This, particular, allows us, same way deterministic setting, conduct systematic approximations and infer different simplified models including natural way.