Existence and stability results for steady atmospheric Ekman flows in ellipsoidal coordinates

Abstract

In this paper, we investigate steady uniform atmospheric Ekman flows in ellipsoidal coordinates. Different from homogeneous system, we retain the influence of pressure on steady uniform atmospheric Ekman flows and establish the non-homogeneous governing equations. These governing equations can also be used to derive the classical equations for geostrophic balance. Further, when the eddy viscosity is the piecewise-constant, we derive a new first-order non-homogeneous differential system. Using the matrix theory, we give the existence and uniqueness of bounded solution to atmospheric Ekman flows, and also present Hyers–Ulam stability. Moreover, we consider atmospheric Ekman flows with constant eddy viscosity with a small perturbation and general periodic variable eddy viscosity, and show more continued results. Finally, we analyze the physical properties of our results.