The kinematic and dynamic boundary conditions on the free surface of a fluid should be posed for water wave problems. In the framework of potential theory for an inviscid and incompressible fluid with an irrotational motion, the combined boundary condition, which involves the velocity potential only, is often used by eliminating the elevation terms mathematically. Such a combination is correct for the solutions in the frequency domain, and is not feasible for an initial-boundary-value problem in the time domain since it leads to a totally different physical formulation. The correct initial conditions for pure gravity waves and hydroelastic waves are presented.

中文翻译：

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关于水波问题的运动学和动态自由表面边界条件的初始值

对于水波问题，应提出流体自由表面的运动学和动态边界条件。在具有无旋运动的不粘且不可压缩的流体的势能理论框架中，通常仅通过数学方式消除高程项来使用仅涉及速度势能的组合边界条件。这样的组合对于频域中的解是正确的，并且对于时域中的初始边界值问题是不可行的，因为它导致了完全不同的物理公式。给出了纯重力波和水弹性波的正确初始条件。