Abstract The viscosity of water induces a vorticity near the free surface boundary. The resulting rotational component of the fluid velocity vector greatly complicates the water wave system. Several approaches to close this system have been proposed. Our analysis compares three common sets of model equations. The first set has a rotational kinematic boundary condition at the surface. In the second set, a gauge choice for the velocity vector is made that cancels the rotational contribution in the kinematic boundary condition, at the cost of rotational velocity in the bulk and a rotational pressure. The third set circumvents the problem by introducing two domains: the irrotational bulk and the vortical boundary layer. This comparison puts forward the link between rotational pressure on the surface and vorticity in the boundary layer, addresses the existence of nonlinear vorticity terms, and shows where approximations have been used in the models. Furthermore, we examine the conservation of mass for the three systems, and how this can be compared to the irrotational case.

中文翻译：

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协调粘性水波的不同公式及其质量守恒

摘要 水的粘性在自由表面边界附近引起涡度。由此产生的流体速度矢量的旋转分量使水波系统大大复杂化。已经提出了几种关闭该系统的方法。我们的分析比较了三组常见的模型方程。第一组在表面具有旋转运动学边界条件。在第二组中，对速度矢量进行了规范选择，以消除运动学边界条件中的旋转贡献，代价是体积中的旋转速度和旋转压力。第三组通过引入两个域来规避这个问题：无旋体和涡旋边界层。这种比较提出了表面旋转压力与边界层涡度之间的联系，解决了非线性涡量项的存在，并显示了模型中使用近似值的地方。此外，我们检查了三个系统的质量守恒，以及如何将其与无旋情况进行比较。