Atmospheric Ekman Flow Varying With Latitude in the Northern Hemisphere

The Coriolis force plays a crucial role in the formation of Ekman currents. Since the Coriolis force varies with latitude, in different latitudinal regions, its degree of action on the fluid is different, which leads to the characteristics of Ekman currents, such as the direction and velocity of the flow, also changing with latitude. In this study, our focal point lies in comprehensively elucidating the intricate relationships among atmospheric Ekman flows, latitude, and height. For the scenario of height-dependent eddy viscosity, by employing a stream function, we meticulously transform the governing equations into a linear elliptic differential equation. Subsequently, through mathematical analysis, we construct a radially symmetric solution. Moreover, in the case of a specific latitude-dependent eddy viscosity, we precisely define the explicit zonal and meridional components of the wind. Based on the expression of the horizontal velocity component, we determine the angle between the wind speed and the geostrophic wind at any altitude. Then, for the specified parameters, we plot the graph of this angle. This enables us to conduct in-depth investigations into their respective meridional structures and vertical (height-related) structures, thereby shedding new light on the complex behaviors of atmospheric Ekman flows under diverse conditions.