Examination on errors of two simplified models for simulating weakly spreading seas

Numerical phase-resolved modelling of random waves on large spatiotemporal scale, meanwhile considering sufficient nonlinearities, is very essential to gain insight of the nonlinear wave-wave interaction process and the mechanism of the so-called rogue waves. To do that, it has been shown that two simplified models, i.e., the fifth order Enhanced Non-Linear Schrödinger Equation (short as ENSLE-5F) and the Quasi-Spectral Boundary Integral (short as QSBI) method, are good alternatives to the fully nonlinear approaches, when the wave steepness is small and/or the spectral bandwidth is narrow [Wang, J., Ma, Q. and Yan, S., 2017. On quantitative errors of two simplified unsteady models for simulating unidirectional nonlinear random waves on large scale in deep sea. Physics of Fluids, 29(6), 067107.]. A criterion for selecting the most efficient model which can achieve sufficient accuracy is proposed in their paper. Furthermore, the errors of the two simplified models for simulating unidirectional waves can be predicted before performing the simulations by using the suggested formulas, if the wave steepness and spectral bandwidth are known in advance. In this paper, the suitability of extending the criterion and the formulas to weakly spreading seas will be explored. It is found that they are not restricted to unidirectional waves, but can also be applied to spreading seas. In addition, the maximum spreading angle for using the criterion or the formulas is presented.