The Rossby Number: How Rotation Affects Ocean Circulation

Abstract

This project investigates how the Rossby number influences ocean circulation. The Rossby number, defined as Ro =U / ( fL) , compares inertial forces to Coriolis forces and determines whether rotation dominates a given flow. Through non-dimensionalization of the Navier-Stokes equations, Ro emerges naturally as the ratio of these two forces. The same scale analysis also yields the Ekman number E =ν / ( fL² ) , which measures the importance of viscous effects relative to rotation. We systematically define Ro and examine three regimes: Ro <<1 , Ro ~1 , and Ro >>1 . Each regime corresponds to different ocean circulation behaviors, from rotation-dominated large-scale currents to rotation-negligible small-scale motions. A typical mid-latitude ocean current yields Ro ~ 0.001 , confirming that rotation is the dominant control in large-scale ocean dynamics.