Exact solutions to the governing equations for atmospheric motion are derived which model nonlinear gravity wave propagation superimposed on atmospheric currents. Solutions are explicitly prescribed in terms of a Lagrangian formulation, which enables a detailed exposition of intricate flow characteristics. It is shown that our solutions are well-suited to modelling two distinct forms of mountain waves, namely: trapped lee waves in the Equatorial f-plane, and vertically propagating mountain waves at general latitudes.

中文翻译：

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非线性大气重力波建模的精确解

推导了大气运动控制方程的精确解，该方程模拟了叠加在大气流上的非线性重力波传播。解决方案是根据拉格朗日公式明确规定的，这使得能够详细阐述复杂的流动特性。结果表明，我们的解决方案非常适合模拟两种不同形式的山波，即：赤道f平面中的受困背风波和一般纬度处的垂直传播山波。