[BUG] curl question

[Kimberly J. Burch]

Dear Tevian,

I was hoping you could clear something up.  We are trying to look at the
curl of a vector field using the paddle wheel argument that we learned at
the workshop.  However, the following vector field is giving us trouble...

F(x,y)= y/(x^2+y^2) i - x/(x^2+y^2) j

If you plot the vector field in Maple you see the vectors are longer near
the origin (and decrease in length as you move away from the origin).  If
you place a paddle wheel in the flow it would seem that since the arrows
are longer at the bottom side of the paddle wheel that the paddle wheel
should spin counter-clockwise.  But, curl=0 by computation! 

One thought we had was that the paddle wheel does turn counter-clockwise
but the clockwise flow of the water negates this motion so that the paddle
wheel does not spin.  I am disappointed if this is the case. If we want
to teach the students a model of how to intuitively understand the curl,
this example seems to break the model.

Sorry to bother you with this.  If you are too busy please feel free to
ignore this.  Between 5 or so professors here you would think we could
come up with a good explanation and yet we all think it should spin!

-Kimberly

-------------------------------------------------------------------------------
Dr. Kimberly Jordan Burch, Assistant Professor
Department of Mathematical Sciences
202 Richardson Hall, Montclair State University
Montclair, NJ 07043
Phone: (973) 655-5184
http://www.csam.montclair.edu/~burch