背景流中沿岸陷波与不稳定性的谱方法
Spectral Methods for Coastal-Trapped Waves and Instabilities in a Background Flow
AI总结：
本文提出一种基于谱方法的数值方法，用于求解背景流和复杂地形下的非静力沿岸陷波及不稳定性特征值问题，并在三个算例中验证了其可靠性，成功识别出东南格陵兰陆架模拟中的沿岸陷波。
摘要：
本文提出了一种数值方法，用于在存在背景流和复杂海岸地形的情况下，求解非静力Boussinesq方程的非静力沿岸陷波和不稳定性解。我们使用谱方法对二维特征值问题进行离散化，并通过标准方法求解所得的离散问题。我们将该方法应用于三个算例，结果表明其与先前的数值和解析结果一致。特别地，我们证明该方法能够可靠地识别出与东南格陵兰陆架真实模拟中所见波动相对应的沿岸陷波解。
英文摘要：
Here we present a numerical method for finding non-hydrostatic coastal-trapped wave and instability solutions to the non-hydrostatic Boussinesq equations in the presence of a background flow and complicated coastal topography. We use spectral methods to discretise the two-dimensional eigenvalue problem and solve the resulting discrete problem by standard methods. Our approach is applied to three examples and shown to be consistent with previous numerical and analytical results. In particular, we show that our method is able to reliably identify coastal-trapped wave solutions that correspond to waves seen in realistic simulations of the Southeast Greenland shelf.
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