Conserved quantities in the Ekman layer

The classical Ekman (1905)'s theory of wind-driven currents at the surface boundary layer is a well-known mathematical model that describes transport phenomena in coastal processes, (e.g.) upwellings and downwellings, and represents an essential part of modern oceanography. Understanding the Ekman layer is important to quantify deviations to observed magnitudes from the classical behavior. In this theoretical work, the Ekman layer is revisited through Noether's theorem. This theorem plays a central role in theoretical physics and Lie group theory showing a direct connection between symmetries and conservation laws. Therefore, the goal of the work is to determine what quantities are conserved in the Ekman layer.