Abstract The Rossby solitary waves in the barotropic vorticity model which contains the topography on the earth’s δ-surface is investigated. First, applying scale analysis method, obtained the generalized quasi-geostrophic potential vorticity equation (QGPVE). Using The Wentzel–Kramers–Brillouin (WKB) theory, the evolution equation of Rossby waves is the variable-coefficient Korteweg–de Vries (KdV) equation for the barotropic atmospheric model. In order to study the Rossby waves structural change to exist in some basic flow and topography on the δ-surface approximation, the variable coefficient of KdV equation must be explicitly, Chebyshev polynomials is used to solve a Sturm-Liouville-type eigenvalue problem and the eigenvalue Rossby waves, these solutions show that the parameter δ usually plays the stable part in Rossby waves and slow down the growing or decaying of Rossby waves with the parameter β.

中文翻译：

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地球δ表面地形的正压Rossby波

摘要 研究了正压涡度模型中包含地球δ表面地形的Rossby孤立波。首先，应用尺度分析方法，得到广义准地转位涡方程（QGPVE）。使用 Wentzel-Kramers-Brillouin (WKB) 理论，Rossby 波的演化方程是正压大气模型的可变系数 Korteweg-de Vries (KdV) 方程。为了研究δ表面近似上某些基本流动和地形中存在的罗斯比波结构变化，KdV方程的变系数必须明确，切比雪夫多项式被用来解决Sturm-Liouville型特征值问题和特征值罗斯比波，