Study of Motions of Point Vortices in a Periodic Box using Mathematica -- from Wolfram Library Archive

Title

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

Downloads

Karman.gif (2.7 MB) - Animated GIF

PDF.gif (20.3 KB) - GIF image

Scattering.gif (23.2 KB) - GIF image

TurbulentPV2.gif (2.8 MB) - Animated GIF

TurbulentPVs.gif (2.9 MB) - Animated GIF

TurbulentSF.gif (10.8 MB) - Animated GIF

Umeki-PointVorticies.nb (774.5 KB) - Mathematica Notebook [for Mathematica 5.2]

VortexSheet.gif (3.4 MB) - Animated GIF

figure1.eps (124.7 KB) - Enhanced postscript file

figure2.eps (131.9 KB) - Enhanced postscript file

figure4a.eps (104 KB) - Enhanced postscript file

figure4b.eps (104 KB) - Enhanced postscript file