论文标题
哈密顿的随机表面波问题的表述
Hamiltonian formulation of the stochastic surface wave problem
论文作者
论文摘要
我们设计了水波问题的随机哈密顿式公式。这种随机表示形式建立在位置不确定性下的建模框架内。从限制到一般随机流体运动方程的自由表面，我们展示了一个人如何自然地推断出小噪声假设下的哈密顿结构。此外，与经典水波理论一样，非本地dirichlet-neumann oberator在能量功能中明确出现。特别是，这使我们以与确定性环境相同的方式进行了迪里奇特 - 尼曼操作员的系统近似，并推断出以自然方式（包括噪声）的不同简化的波浪模型。
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.
