深水交叉表面波中的虚波应力
Virtual wave stress in deep-water crossed surface waves
摘要：
由于流体粘性，在深水表面上激发的波浪在时间和/或空间上衰减，并且与波动相关联的动量通过虚拟波应力的作用从波浪传递到欧拉慢流。在这里，基于总动量守恒，我们找到了虚拟波应力平静重力波的假设下，缓慢的欧拉流是弱的，在这个意义上的弗劳德数是小的，表面波的散射慢流不均匀性可以忽略不计。特别地，我们计算了由一个传播波和两个正交的驻波产生的虚波应力。所得结果具有欧拉不变性，是与以前已知的一致，并推广到几乎单色波在任意方向传播的激发的情况下。
英文摘要：
Waves excited on the surface of deep water decay in time and/or space due to the fluid viscosity, and the momentum associated with the wave motion is transferred from the waves to Eulerian slow currents by the action of the virtual wave stress. Here, based on the conservation of the total momentum, we found the virtual wave stress produced by calm gravity waves under the assumption that the slow Eulerian currents are weak in the sense that the Froude number is small and the scattering of surface waves by slow flow inhomogeneities can be neglected. In particular, we calculated the virtual wave stress generated by a propagating wave and two orthogonal standing waves. The obtained results possess Euler invariance, are consistent with previously known ones, and generalize them to the case of the excitation of almost monochromatic waves propagating in arbitrary directions.
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