Constant vorticity atmospheric Ekman flows in the $ f- $plane approximation

Abstract

<p style='text-indent:20px;'>We study the geophysical fluid dynamical 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 <inline-formula><tex-math id="M2">\begin{document}$ f- $\end{document}</tex-math></inline-formula>plane approximation. For non-equatorial <inline-formula><tex-math id="M3">\begin{document}$ f- $\end{document}</tex-math></inline-formula>plane approximation, we show that any bounded solution of the Ekman flow with a flat surface and constant vorticity vector is the stationary flow with vanishing velocity field, while for the equatorial <inline-formula><tex-math id="M4">\begin{document}$ f- $\end{document}</tex-math></inline-formula>plane approximation, we obtain that the pressure presents no variation in the northward direction and the meridional component is constant throughout the fluid domain.</p>