How to make a computer-generated sketch of the path of a fluid element (tornado)?

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Kenny Greene
Kenny Greene 2017-9-22
Problem statement:
In a plane parallel to and near the ground, the velocity components of a tornado centered at the origin are
V_r = (-a/r), V_theta = (b/r)
where a = 100 m^2/s and b = 1000 m^2/s. These equations are valid for r > r_eye = 20 m. For r < r_eye, in the eye of the tornado, assume that the air rotates as a rigid in the plane parallel to the ground and that it has a constant vertical (z) velocity upwards.
What I have found through calculations:
I know the circulation rate of the tornado for Radius R > r_eye -2000*pi m/s^2 and that the flow is irrotational and incompressible.
I know at time t=0, a fluid element is located at (x,y) = (0,100m) and that it will take 48 seconds for the fluid element to reach the outer part of the eye of the tornado.
I know that the location of the fluid element when it first reaches the tornado eye is theta = 17.67 rad.
The final part tells me that I must provide a computer-generated sketch of the patch of the fluid element in the previous parts. This seems like a very easy task but I am having trouble combining everything I have found to sketch a circular path. Is there some kind of sketch path function?
Any help will be greatly appreciated. Thanks in advance!

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