Is the Derivation of Ekman Transport Correct with These Assumptions?

[ATY]

Hey guys,
I need your help.
We tried to derive the ekman transport in a lecture. The assumptions we made are
1. constant density
2. stationarity
3. no horizontal pressure gradient and no horizontal velocity gradient
4. no vertical velocity.
So this is what the professor showed us:

But is this correct ? I thought that from stationarity we get [itex]\frac{\partial}{\partial t}=0[/itex] instead of [itex]\frac{d}{dt} = 0[/itex].
I would still get to the correct result using
[itex]\frac{\partial u}{\partial x}=\frac{\partial v}{\partial x}=\frac{\partial v}{\partial y}=\frac{\partial v}{\partial x}=0[/itex] and [itex]w=0[/itex] in order to eliminate all terms on the left side of the equation.
Can somebody help me ?

 

[gtoguy97]

Yes, you are correct. The professor should have used the partial derivative in place of the ordinary (total) derivative. Using the assumptions you listed, you can indeed derive the Ekman transport equation by setting all of the derivatives equal to zero. This can be done by setting the horizontal pressure gradient and horizontal velocity gradient to zero, and setting the vertical velocity to zero.