The aim of this paper is to prove real analytic properties of all streamlines of two‐dimensional steady rotational gravity water waves in two‐layer flows. Provided that there are no stagnation points in the flow, we show that each streamline, including the free surface and the interface, is a real analytic curve if the height function is in , which corresponds to an arbitrarily bounded and measurable vorticity function. Our results generalize those for the situation of single layer flow, and improve the results in the work by Chu, Escher, and Wang [Analyticity of rotational travelling waves in two‐layer flows, submitted], where the analyticity is obtained for rotational two‐layer water waves when the height function is in corresponding to a Hölder continuous vorticity function.

中文翻译：

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旋转行进重力两层波的解析性

本文的目的是证明两层流中二维稳定旋转重力水波的所有流线的真实解析特性。假设流中没有停滞点，则表明如果高度函数位于，则包括自由曲面和界面在内的每条流线都是真实的分析曲线，它对应于任意有界且可测量的涡度函数。我们的结果将这些结果推广到单层流的情况，并改进了Chu，Escher和Wang [提交的两层流中的旋转行波的解析性]的结果，其中获得了旋转两层流的解析性。当高度函数对应于Hölder连续涡度函数时，水层会起波浪作用。