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.
Accurately modelling the gravity surface waves in laboratory or numerical wave tank (NWT) environment can be beneficial to many aspects of human's oceanic activities, e.g., wave forecast, coastal protection, nautical practice, gas/oil exploitation, renewable energy, etc. To describe steady waves that feature unchanged periodical profiles in space and time, linear wave theory, Stokes wave model in finite and deep water, cnoidal and solitary wave model in shallow water are suggested, which have been widely accepted in industry standards. Their applicability within breaking limit in terms of the wave steepness and relative water depth is discussed by Le Méhauté (1976), which is reproduced and shown in Fig. 1. More recently, a unified model, i.e., the renormalized cnoidal wave theory (Clamond, 2003), that combines the aforementioned steady wave models, and also account for the recently discovered spike waves (Gandzha & Lukomsky, 2002), is suggested, which overcomes the non-uniformity of Stokes wave and shallow water wave models over the complete range of water depth.
