a1 Mathematics Department, Brown University, Box 1917, Providence, RI 02912, USA
Two-dimensional, finite-depth periodic steady water waves with variable vorticity ω=γ(ψ) and large amplitude a are computed for a large number of cases. In particular, the effect of a shear layer at the top, the middle or the bottom is considered. The maximum amplitude amax varies monotonically with the vorticity function γ(ċ). It is increasing if the stagnation point is at the crest, and is decreasing if the stagnation point is in the interior of the fluid or on the bottom. Relationships between the amplitude, hydraulic head, depth and mass flux are investigated.
(Received October 15 2007)
(Revised April 07 2008)