Gerris在海洋大振幅内孤立波数值模拟中的应用

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(Synthetic Aperture Radar)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。

APPLICATION OF GERRIS IN NUMERICAL SIMULATION OF OCEAN LARGE-AMPLITUDE INTERNAL SOLITARY WAVES

The fully nonlinear steady-state large-amplitude internal solitary waves in continuously stratified fluids were simulated in Gerris, an open source fluid dynamics software, based on the 2D incompressible Euler equations with Boussinesq approximation. The comparison of internal waves simulated by the Euler model and by the KdV model indicates that high-order nonlinear terms should not be neglected when large-amplitude is concerned. The simulation of internal waves by the Euler model reveals that the half width of isopycnic surface of a fully nonlinear large-amplitude internal solitary wave varies with depth, which makes the method 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 doubtful. Therefore, the retrieval method is necessary to be reassessed. In addition, the validity of the Euler model implemented by Gerris to simulate internal solitary waves has been verified by two sets of in-situ measurements.