Change in the height of a fluid vortex

[Rainbrew]

I'm currently struggling slightly with finding some information regarding a vortex. If I have a fluid in a cylindrical container and the fluid is then rotated at a constant speed, the vortex will displace the water and raise it relative to the initial level of the fluid. Is there any formula describing this change in height taking into consideration the viscosity of the fluid? I've been digging for some time now and cannot find anything on this, I'd really appreciate some help. Thanks in advance!

 

[Nidum]

There is a large amount of information available on this general subject . Just search on Vortex / Free Vortex / Forced Vortex ?

Here is a very basic introduction to the topic

Really though it is not too difficult to derive the necessary equations from first principles .