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Gerris在海洋大振幅内孤立波 数值模拟中的应用
曾侃, 李恒宇
中国海洋大学
摘要:
本文运用基于自适应网格的流体动力学开源软件Gerris来建立基于Boussinesq近似下的二维不可压缩Euler方程组的数值模型以模拟不同层化条件下稳定状态的完全非线性大振幅内孤立波。文中比较了完全非线性的用Gerris实现的Euler模型与弱非线性的KdV理论模型在刻画大振幅内孤立波结构及特征参数上的差异,说明在模拟大振幅内孤立波时,高阶非线性不应忽略。Euler模型模拟结果表明完全非线性大振幅内孤立波的等密度面半宽度随深度变化,这使得基于KdV方程解析解,利用卫星SAR图像提取内孤立波极值间距来反演内波振幅的可行性存疑,需要重新评估。此外,本文用两组实测数据验证了用Gerris实现的Euler模型模拟大振幅内波的有效性。
关键词:  大振幅内孤立波  数值模拟  欧拉模型  Gerris
DOI:10.11693/hyhz20181200283
分类号:
基金项目:中国空间技术研究院基金
APPLICATION OF GERRIS IN NUMERICAL SIMULATION OF OCEAN LARGE-AMPLITUDE INTERNAL SOLITARY WAVES
Zeng Kan, Li Heng Yu
Ocean Univeristy of China
Abstract:
The simulation of fully nonlinear steady-state large-amplitude internal solitary waves in continuously stratified fluids based on the 2D incompressible Euler equations with Boussinesq approximation is carried out with Gerris, an open source fluid dynamics software. The large-amplitude solitary wave structure and characteristic parameters simulated by the fully nonlinear Euler model and by the weakly nonlinear KdV model are compared., The results indicate that high-order nonlinear terms should not be neglected when large-amplitude are concerned for studying internal solitary wave.The results simulated by Euler model reveal that the half width of isopycnic surface of a fully nonlinear large-amplitude internal solitary wave varies with depth, which makes it doubtful to retrieve the internal wave amplitude using the distance between two extreme values of internal wave pattern extracted from a spaceborne SAR image based on the analytical solution of the KdV equation. Therefore, the retrieval method is necessary to be reassessed. The validity of Euler model implemented by Gerris is tested by two sets of in-situ measurements of internal waves.
Key words:  large-amplitude internal solitary wave  numerical simulation  Euler model  Gerris
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