论文标题
保留经典水波理论随机扰动的结构
A structure preserving stochastic perturbation of classical water wave theory
论文作者
论文摘要
在流体问题方程式中包含随机术语，可以使过程的统计表示，这些过程未通过数值计算解决。在这里，我们使用一种方法来得出表面重力波的行为的随机方程，该方法旨在保留表面下流体运动方程的几何结构。在这样做的过程中，我们发现了一个随机方程，用于速度潜力的演变，更重要的是，表明水波动力学的随机方程具有哈密顿结构，这反映了扎卡罗夫（Zakharov）在确定性理论中发现的。这涉及速度场的扰动，与确定性速度不同，该问题不必与问题结束。
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. Here, we derive stochastic equations for the behaviour of surface gravity waves using an approach which is designed to preserve the geometric structure of the equations of fluid motion beneath the surface. In doing so, we find a stochastic equation for the evolution of a velocity potential and, more significantly, demonstrate that the stochastic equations for water wave dynamics have a Hamiltonian structure which mirrors that found by Zakharov for the deterministic theory. This involves a perturbation of the velocity field which, unlike the deterministic velocity, need not be irrotational for the problem to close.
