Gravity water flows with discontinuous vorticity and stagnation points

This is the authors' abstract. We don't add key points for this paper.

We construct small-amplitude steady periodic gravity water waves arising as the free surface of water flows that contain stagnation points and possess a discontinuous distribution of vorticity in the sense that the flows consist of two layers of constant but different vorticities. We also describe the streamline pattern in the moving frame for the constructed flows.