随机表面波问题的Hamilton形式
Hamiltonian formulation of the stochastic surface wave problem
摘要：
我们设计了一个随机哈密顿制定的水波问题。这种随机表示是建立在位置不确定性下的建模框架内。从一般随机流体运动方程的自由面约束出发，我们展示了如何在小噪声假设下自然地推导出哈密顿结构。此外，在经典的水波理论中，非局部Dirichlet-Neumann算子出现明确的能量泛函。特别是，这使我们能够以与确定性设置相同的方式对狄利克雷-诺依曼算子进行系统近似，并以自然的方式推断出包括噪声在内的不同简化波模型。
英文摘要：
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.
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