Variational formulations for steady water waves with vorticity - CONSTANTIN, ADRIAN; SATTINGER, DAVID; STRAUSS, WALTER (Journal of fluid mechanics, 2006)
For free-surface water flows with a vorticity that is monotone with depth, we show that any critical point of a functional representing the total energy of the flow adjusted with a measure of the vorticity, subject to the constraints of fixed mass and horizontal momentum, is a steady water wave.