Interaction of Nonlinear Water Wave and Nonuniform Currents

Abstract

In this chapter, we illustrate the validity of the homotopy analysis method (HAM) for a complicated nonlinear PDE describing the nonlinear interaction of a periodic traveling wave on a non-uniform current with exponential distribution of vorticity. In the frame of the HAM, the original highly nonlinear PDE with variable coefficient is transferred into an infinite number of much simpler linear PDEs, which are rather easy to solve. Physically, it is found that Stokes' criterion of wave breaking is still correct for traveling waves on non-uniform currents. It verifies that the HAM can be used to solve some complicated nonlinear PDEs so as to deepen and enrich our physical understanding about some interesting nonlinear phenomena.