From AMS Glossary
Explicitly, the vertical Ekman number is
in which Kv is the vertical eddy viscosity, f the Coriolis parameter, and D the characteristic vertical length scale. The horizontal Ekman number is
in which Kh is the horizontal eddy viscosity and L is the characteristic horizontal length scale. The Ekman number gives a measure of the rate at which stresses at a boundary (e.g., wind-induced stresses at the ocean surface) are communicated to the fluid interior.