Chapter 7 - Some Mathematics:
The Equations of Motion

7.2 Coordinate System

Coordinate systems allow us to find locations in theory and practice. Various systems are used depending on the size of the features to be described or mapped. I will refer to the simplest systems; descriptions of other systems can be found in geography and geodesy books.

1. Cartesian Coordinate System is the one I will use most commonly in the following chapters to keep the discussion as simple as possible. We can describe most processes in Cartesian coordinates without the mathematical complexity of spherical coordinates. The standard convention in geophysical fluid mechanics is x is to the east, y is to the north, and z is up.
   
   f-Plane is a Cartesian coordinate system in which the Coriolis force is assumed constant. It is useful for describing flow in regions small compared with the radius of the Earth and larger than a few tens of kilometers.
   
   β-plane is a Cartesian coordinate system in which the Coriolis force is assumed to vary linearly with latitude. It is useful for describing flow over areas as large as ocean basins.
   
   
2. Spherical coordinates are used to describe flows that extend over large distances and in numerical calculations of basin and global scale flows.

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