Large Amplitude Steady Periodic Waves for Fixed-Depth Rotational Flows

We consider steady periodic water waves with vorticity which propagate over a flat bed with a specified fixed mean-depth d > 0. Following a novel reformulation of the governing equations, we use global bifurcation theory to establish a global continuum of solutions throughout which the mean-depth is a fixed quantity. Furthermore, we establish the limiting behavior of solutions in this continuum, which include the existence of weak stagnation points, that are characteristic of large-amplitude steady periodic water waves.