On quantitative errors of two simplified unsteady models for simulating unidirectional nonlinear random waves on large scale in deep sea
On quantitative errors of two simplified unsteady models for simulating unidirectional nonlinear random waves on large scale in deep sea
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DOI：
10.1063/1.4989417
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发表时间：
2017-06
影响因子：
4.6
通讯作者：
Jinghua Wang;Q. Ma;S. Yan
中科院分区：
文献类型：
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作者：
Jinghua Wang;Q. Ma;S. Yan
为了研究非线性随机波浪动力学或统计学，通常采用简化的数值模型，如基于非线性薛定谔方程(NLSE)的数值模型，在大空间和长时间尺度上对深海中的非线性随机波进行直接的相分辨数值模拟。它们是有效的，在许多情况下可以给出足够可接受的结果，但它们是通过假设窄带宽和小陡度而得到的。到目前为止，还没有精确预测这种简化模型的定量误差的公式。本文将给出基于傅里叶变换和准谱边界积分法的增强NLSE在大空间和长时间尺度(约128个峰值波长和1000个峰值周期)上模拟海浪时的误差估计公式。这些公式是通过对简化模型的误差进行拟合得到的，这些误差是通过将简化模型的波高与用来模拟由两个常用的参数范围较大的海浪谱定义的初始条件的完全非线性模型得到的结果进行比较而得到的。在此基础上，给出了简化模型的适用范围。
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 Schrodinger 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.