On quantitative errors of two simplified unsteady models for simulating unidirectional nonlinear random waves on large scale in deep sea

Abstract

To investigate nonlinear random wave dynamics or statistics, direct phase-resolved numerical simulation of nonlinear random waves in deep sea on large-spatial and long-temporal scales are often performed by using simplified numerical models, such as those based on the Nonlinear Schrödinger Equation (NLSE). They are efficient and can give sufficiently acceptable results in many cases but they are derived by assuming narrow bandwidth and small steepness. So far, there has been no formula to precisely predict the quantitative errors of such simplified models. This paper will present such formulas for estimating the errors of enhanced NLSE based on the Fourier transform and quasi spectral boundary integral method when they are applied to simulate ocean waves on large-spatial and long-temporal scales (about 128 peak wavelengths and 1000 peak periods). These formulas are derived by fitting the errors of the simplified models, which are estimated by comparing their wave elevations with these obtained by using a fully nonlinear model for simulating the cases with initial conditions defined by two commonly used ocean wave spectra with a wide range of parameters. Based on them, the suitable regions for the simplified models to be used are shown.