On some properties of velocity field for two dimensional rotational steady water waves. (July 2019) - Basu, Biswajit
Abstract: We investigate the properties of velocity field for steady periodic water waves over a flat bed for a generalized class of C 1 vorticity functions γ . Results are proved by exploiting the maximum principles and are based on Dubreil–Jacotin transformation of the fluid domain. Some properties of velocities interior to the fluid domain and the locations of maximum/minimum horizontal fluid velocities are investigated and proved for rotational water waves without any restriction to amplitude. For u < c and a monotonically varying positive vorticity ( γ = u y − v x ≥ 0 ), the location of maximal horizontal velocity has been proven to be the crest, generalizing some of the recently proved results.