  We numerically investigate the flow structure of periodic steady water waves
of fixed relative mass flux propagating on rotational flows with piece-wise
constant vorticity. We show that for wave solutions along the global
bifurcation diagram the stagnation point can first occur internally or at the
bottom, and then again occurs at the crest with further increase in wave
height. We observe that the bifurcation diagram has a new branch which is not
connected to the trivial solution. Furthermore, we present an in-depth
discussion of the results on pressure distributions and particle trajectories
beneath large-amplitude steady waves near stagnation. We also expand on
previous results concerning the amplitude and mass flux of steady water waves
traveling on rotational flows with discontinuous vorticity.
