We consider steady symmetric gravity water waves on finite depth with constant vorticity and a monotone surface profile between crests and troughs. The problem is transformed into one concerning the vertical velocity. A representation formula for the stream function in terms of the surface and the vorticity is presented, and we show that the surface can be determined from the vertical velocity. © 2007 Elsevier Inc. All rights reserved.
Ehrnström, M. (2008). A new formulation of the water wave problem for Stokes waves of constant vorticity. Journal of Mathematical Analysis and Applications, 339(1), 636–643. https://doi.org/10.1016/j.jmaa.2007.07.022