# Ekman Surface Pumping in Polar Coordinates?

1. Apr 15, 2013

### xtamx

Hello,

I am working on a question in a GFD textbook about tea leaves collecting in the center of the cup regardless of the direction that the tea is stirred. I have an idea of why this is the case but to prove it I need to convert the equation for Ekman pumping to polar coordinates. Its given as:

w = 1/ρf (∂τy/∂x - ∂τx/∂y)

where w is the fluid velocity in the vertical direction
ρ is the fluid density
f is the Coriolis parameter (or rotation rate in the tea cup)
τx and τy are the stresses on the fluid from the walls of the cup

The stress from the bottom of the cup is always going to be in the angular direction in polar coordinates so the net transport will always be in the radial direction according to Ekman dynamics. If the polar version of the above equation is similar then the sign on f changes to negative then the sign on τθ also changes and w remains upward.

The problem is that I have no idea how to convert that to polar coordinates. Can anyone help?