We make a physical–mathematical analysis of the implications that the presence of a large number of tiny bubbles may have, when present, on the thin upper layer of the sea. In our oceanographic example, the bubbles are due to intense rain. It was found that the bubbles increase momentum dissipation in the near surface and affect the surface tension force. For short waves, the implications of increased vorticity are momentum exchanges between wave and mean flow and modifications to the wave dispersion relation. For the direct effect we have analyzed, the implications are estimated to be non-significant when compared to other processes of the ocean. However, we hint at the possibility that our analysis may be useful in other areas of research or practical application.

中文翻译：

---

夹带空气对海浪的影响

我们对大量微小气泡的存在（当存在时）对薄薄的海洋上层的影响进行了物理数学分析。在我们的海洋学示例中，气泡是由于大雨造成的。发现气泡增加了近表面的动量耗散并影响表面张力。对于短波，涡度增加的含义是波和平均流之间的动量交换以及波色散关系的修改。对于我们分析的直接影响，与海洋的其他过程相比，其影响估计不显着。然而，我们暗示了我们的分析可能在其他研究领域或实际应用中有用的可能性。