# Parametric Equation of a Particle Movement inside a Vortex in a Rectangular Box

I am trying to simulate the movement of a particle in a vortex in a rectangular box, I am currently using an ellipse but that causes the particle to collide with the walls more that I want.

The equation doesn't have to be exact, I am thinking for instance in to augment or reduce the mayor and minor diameter of my ellipse accordingly to, let's say the angle t in relation to angle a

I just wanted to know whether there is some equation that descrives that trajectory

Also, I want to be able to calculate the tangent vector

The following image shows what I've mentioned

http://s14.postimage.org/8cmzwwx8x/Untitled_1.png

Any help is appreciated

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Is it a point vortex at the center of the box, or is vorticity uniformly distributed over all of the interior? – Rahul Oct 16 '12 at 9:59
I guess is a vorticity uniformly distributed, think of a outboard motor in the x axis near one wall pointing up or down side the y axis, in that case the tangent vector magnitud could be proportional to the angle t – rraallvv Oct 16 '12 at 17:56

How about a superellipse (with $n = 4$ or $n = 6$, say): http://en.wikipedia.org/wiki/Superellipse