We present an approach that facilitates the generation of explicit solutions to atmospheric Ekman flows with a height-dependent eddy viscosity. The approach relies on applying to the governing equations, of Sturm–Liouville type, a suitable Liouville substitution and then reducing the outcome to a nonlinear first-order differential equation of Riccati type.

中文翻译：

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大气边界层动力学中的Sturm-Liouville问题

我们提出了一种方法，该方法有助于生成具有高度依赖的涡流粘度的大气埃克曼流的明确解决方案。该方法依赖于应用Sturm–Liouville类型的控制方程式，适当的Liouville替代，然后将结果简化为Riccati类型的非线性一阶微分方程。