Abstract
In this paper, we study the atmospheric Ekman flows of the Northern Hemisphere related to latitude and height in ellipsoidal coordinates. Firstly, by using a suitable transformation, we convert the atmospheric Ekman equation into a second order elliptic partial differential equation. Further, we prove it is equivalent to a second order homogeneous ordinary differential equation with variable coefficients. Finally, we construct the explicit solution and give the laws of motion of the atmospheric Ekman flows.
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