In this section, we will take the Navier-Stokes equation that was developed for fluid mechanics on everyday scales, and consider how it must be modified to represent large scale motions in a geophysical fluid like the ocean and atmosphere. We prefer to write our equations from our own perspective in the traditional local Cartesian system, but this coordinate system is rotating around the Earth.
In a rotating reference frame there are two apparent forces on water parcels that do not exist in a non rotating reference system – the centrifugal force, and the Coriolis force. The idea of an “apparent force” is easiest to think about in a linearly accelerating reference frame, like a moving car. Imagine driving down the road with a helium balloon in the passenger seat. Hit the brakes. What happens to the balloon? It has motion relative to the reference frame of the car that can be accounted for by adding an apparent force resulting from the deceleration of the coordinate system.
The centrifugal force is part of the background of all particles on the Earth and we do not see it in our momentum equation. However, the Coriolis force becomes prominent in the horizontal equations for fluid motion on large scales. We will study two primary steady-state force balances in the ocean that involve the Coriolis force: the Ekman balance (applicable to boundary layers at the top and bottom of the ocean) and geostrophic balance (applicable to the interior ocean between these boundary layers).