Numerical modeling of nonlinear wave transformation using elliptic mild slope equation

Elliptic mild slope equation based models are widely used to compute wavefields in regions of complex, arbitrarily varying topography and geometry. They are used in applications involving wave reflection, diffraction, refraction, nearshore breaking and frictional dissipation. However, these are based on linear wave theory; therefore, nonlinear interactions among frequency components are ignored. In this study, a modified form of the nonlinear elliptic mild-slope equation is used to numerically model the nonlinear wave transformation. The Alternating Direction Implicit (ADI) scheme is employed to solve the equation with appropriate boundary conditions. The nonlinear energy transfer among frequency components, are modeled in the presence of wave reflection, diffraction, refraction, etc. In addition, transformation of wave spectra is studied by incorporating the effects of wave breaking. The computations are compared with the laboratory data and other results. Overall the model performs reasonably well and has improved applicability in comparison to the mild slope models based on parabolic approximation. Copyright © 2013 by the International Society of Offshore and Polar Engineers (ISOPE).

Numerical modeling of nonlinear wave transformation using elliptic mild slope equation Conference Paper