Avoiding polar singularity in ocean modelling.

 In general singularity is  a point at which a given mathematical function is not defined. When numerically modelling oceans we come across with the two poles that can be considered as singularity points. 

There are several methods to deal with the singularity points. However in my work we are only concerned about the Arctic pole. We deal with it by rotating the North pole in to the equator. It should be mentioned that this rotation affects the Coriolis force.  I will discuss later how to rectify this affect.

To rotate the coordinates -90 degrees about the y axis we use Euler rotation Matrix. Given the rotation angle is tita the matrix can be represented as below.

Rotation Matrix