Deflection of an elliptically loaded vortex sheet by a flat plate

We investigate the behavior of vortex flows in the presence of obstacles using numerical simulations. Specifically, we simulate the evolution of an elliptically loaded vortex sheet in the presence of a stationary flat plate in its path. The plate is represented by a number of point vortices whose strength is such that they cancel the normal fluid velocity on the plate. The sheet is approximated by a number of smoothed point vortices called vortex blobs. The resulting system of ordinary differential equations is solved using the 4th order Runge-Kutta method. In our simulations, we vary the initial distance d from the vortex sheet to the plate, the angle φ of the plate relative to the sheet, and the numerical smoothing parameter δ. We study the effects these parameters have on the vortex sheet evolution, including the positions of the vortex centers and the vortex sheet midpoint. We also compare with results derived from a simpler model using only two point vortices instead of a whole sheet. Our main conclusions regard the effect of the distance d, which reduces the total distance traveled as it is increased, and the angle φ, which significantly affects the vortex trajectory after it encounters the plate. Acknowledgements: I thank Professor Monika Nitsche for her guidance in this research. I also thank Professor Robert Krasny for suggesting the problem studied, and Dr. Robert Niemeyer for comments on the manuscript. Finally, I thank the National Science Foundation for supporting this research through the NSF-MCTP program, Mentoring through Critical Transition Points, at the University of New Mexico, via the NSF Award # DMS-1148801. Page 108 RHIT Undergrad. Math. J., Vol. 15, No. 1