标题： 非线性二维水波与任意涡度 显示英文标题

标题： Nonlinear two-dimensional water waves with arbitrary vorticity

摘要： 我们考虑在具有平坦床和自由表面的流体体积中，具有一般非零旋度场的二维水波问题。 所选表面和体积变量的运动非线性方程通过Dirichlet-Neumann算子和流体区域中拉普拉斯算子的格林函数来表示。 此外，我们提供了这两个对象的新显式表达式。 点涡场及其与自由表面的相互作用作为一个例子进行研究。 在小振幅长波Boussinesq和KdV范围内，我们得到了描述点涡动力学和自由表面变量时间演化的耦合方程组。 显示英文摘要

摘要： We consider the two-dimensional water-wave problem with a general non-zero vorticity field in a fluid volume with a flat bed and a free surface. The nonlinear equations of motion for the chosen surface and volume variables are expressed with the aid of the Dirichlet-Neumann operator and the Green function of the Laplace operator in the fluid domain. Moreover, we provide new explicit expressions for both objects. The field of a point vortex and its interaction with the free surface is studied as an example. In the small-amplitude long-wave Boussinesq and KdV regimes, we obtain appropriate systems of coupled equations for the dynamics of the point vortex and the time evolution of the free surface variables.