In this paper, we study the classical problem of the wind in the steady atmospheric Ekman layer with constant eddy viscosity. Three dimensional Ekman flows with constant vorticity is considered in the \(\beta \)-plane approximation. It is remarkable that we explore a totally new approach, which is much different from procedure in (Martin J Fluid Mech 865:762–774, 2019; Chu and Yang J Differ Equ 269:9336–9347, 2020), to show that any Ekman flow with a flat surface and constant vorticity vector is the stationary flow with vanishing velocity field.

中文翻译：

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$$\beta $$ β -Plane Approximation 中的恒定涡度 Ekman 流

在本文中，我们研究了具有恒定涡粘性的稳定大气 Ekman 层中风的经典问题。在\(\beta \)平面近似中考虑具有恒定涡量的三维 Ekman 流。值得注意的是，我们探索了一种全新的方法，它与 (Martin J Fluid Mech 865:762–774, 2019; Chu and Yang J Differ Equ 269:9336–9347, 2020) 中的程序大不相同，以表明任何具有平坦表面和恒定涡量矢量的 Ekman 流是具有消失速度场的静止流。