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Study of Motions of Point Vortices in a Periodic Box using Mathematica
Author

Makoto Umeki
Conference

2006 Wolfram Technology Conference
Conference location

Champaign IL
Description

An assembly of point vortices is a simple and idealized system of the two-dimensional fluid flow. If the number of vortices is larger than three, the system shows chaotic and turbulent motions. The complex expression of the velocity in a periodic box is given by the Weierstrass zeta function as w=u+iv=ia-i Omega z where the bar denotes the complex conjugate. The equation for N point vortices of strength 2 Pi a is written as aa= aaw(a-a).

Mathematica enables us to compute the Weierstrass zeta function as we compute the sinusoidal function in a Fortran code.
Subjects

*Applied Mathematics > Visualization
*Mathematica Technology > Programming > 2D Graphics
*Mathematica Technology > Programming > Animations
*Science > Physics > Fluid Mechanics
Keywords

fluid flow, Weierstrass zeta function, point vorticies
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Karman.gif (2.7 MB) - Animated GIF
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PDF.gif (20.3 KB) - GIF image
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Scattering.gif (23.2 KB) - GIF image
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TurbulentPV2.gif (2.8 MB) - Animated GIF
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TurbulentPVs.gif (2.9 MB) - Animated GIF
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TurbulentSF.gif (10.8 MB) - Animated GIF
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Umeki-PointVorticies.nb (774.5 KB) - Mathematica Notebook [for Mathematica 5.2]
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VortexSheet.gif (3.4 MB) - Animated GIF
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figure1.eps (124.7 KB) - Enhanced postscript file
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figure2.eps (131.9 KB) - Enhanced postscript file
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figure4a.eps (104 KB) - Enhanced postscript file
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figure4b.eps (104 KB) - Enhanced postscript file