The Ekman spiral in primitive equations with wind-driven boundary conditions and Coriolis force

Abstract

In this article we investigate the relationship of the 3D incompressible, primitive equations with wind-driven boundary conditions and Coriolis force and the Ekman spiral. We identify three distinct regimes. In the first one, we show that every solution converges exponentially fast to the Ekman spiral as $t\to +\infty$. In particular, this implies that the Ekman spiral is the unique equilibrium of the system. In the second regime, we prove nonlinear stability of the Ekman spiral, and in the third one, we show nonlinear instability of the Ekman spiral.

arXiv commentExtended version. Generalized main result. Accepted for Publication