Solitary water waves propagating on an underlying uniform current over a finite depth

Abstract

We investigate the nature of velocity and pressure fields for solitary water waves (without any restriction on amplitude) propagating over finite depth with uniform underlying currents. We show that two cases exist corresponding to the fluid velocities u greater than or less than the solitary wave propagation speed c, and these two cases result in different nature of flow fields. We prove the conditions for existence of solitary waves in 2D with uniform underlying current over finite depth for these two cases. We also derive some bounds on Froude number and maximum amplitude of solitary wave height.