Surely the interface cannot be 1/r^2 - as we move towards the centre of the vortex (where r=0) we have an increasing function describing the height of the liquid. ?
Ben - agree about the simplifying assumptions. Will need to brush up on the calculus of variations topic though! Do you have any good references to the technique? I understand the basics but have never applied the tool in anger. Also, not sure about the parabola. If you go and stir some coffee...
Andy, not sure what you mean by "interface goes as 1/r^2". Which interface are you referring to? But thanks for the response. I did not think in terms of a sophisticated fluid flow model for this - this is just an interesting problem I have thought about and to which I would want to apply some...
I hope someone can help with this - its been driving me mad for a while now!
You will have noticed the shape coffee (or whatever liquid) takes when you stir it. Clearly a vortex getting deeper and steeper the faster it is stirred.
So - here's my problem. What's the equation that defines...