HOS Simulations of Nonlinear Water Waves in Complex Media

Abstract

We present an overview of recent extensions of the high-order spectral method of Craig and Sulem (J Comput Phys 108:73–83, 1993) to simulating nonlinear water waves in a complex environment. Under consideration are cases of wave propagation in the presence of fragmented sea ice, variable bathymetry and a vertically sheared current. Key components of this method, which apply to all three cases, include reduction of the full problem to a lower-dimensional system involving boundary variables alone, and a Taylor series representation of the Dirichlet–Neumann operator. This results in a very efficient and accurate numerical solver by using the fast Fourier transform. Two-dimensional simulations of unsteady wave phenomena are shown to illustrate the performance and versatility of this approach.