Streamlines vs. Trajectories in a Translating Rankine Vortex

by Lucas Harris and Dale Durran

Consider a Rankine vortex as shown below. Outside the vortex boundary (indicated by the blue circle), the tangental velocity drops off with distance from the center like 1/r, while inside it increases linearly with radius.

Stationary vortex

Now, let's superimpose a uniform flow from the left onto the vortex where the flow speed is the same as the maximum tangental speed of the vortex.

Vortex and flow

Finally, let's look at the streamlines for this combined flow (in red):

Vortex, flow, and streamlines

Now, let's put this flow into motion and follow the trajectories of three fluid particles.

Last edited 17 October 2006

This material is based upon work supported by the National Science Foundation under Grant No. ATM-0225441.