Solitary waves on flows with an exponentially sheared current and stagnation points

Summary While several articles have been written on water waves flows with constant vorticity, little is known about the extent to which a non-constant vorticity affects flow structure, such as appearance of stagnation points. In order shed light this topic, we investigate in detail beneath solitary propagating an exponentially decaying sheared current. Our focus analyse numerically emergence For purpose, approximate velocity field within fluid bulk through classical Korteweg-de Vries asymptotic expansion and use Matlab language evaluate resulting stream function. findings suggest that can 0, 1 or 2 points body. We also study bifurcation between these flows. simulations indicate emerge from streamline sharp corner.