Be the first to rate this file! 24 downloads (last 30 days) File Size: 816.4 KB File ID: #19306

Kirchhoff Vortex Contour Dynamics Simulation

24 Mar 2008 (Updated 31 Mar 2008)

No BSD License

Contour dynamics simulation of an elliptical vortex in 2D inviscid and incompressible flow

File Information
Description	A Kirchhoff elliptic vortex is a 2D elliptical region (or “patch”) of uniform vorticity embedded in an inviscid, incompressible and irrotational fluid. G. Kirchhoff showed that these are exact solutions to the nonlinear Euler equations in 1876. Subsequently, A. E. H. Love analyzed the linear stability of Kirchhoff vortices, and established that at large aspect ratios they are unstable. He also obtained analytic expressions for the oscillation frequencies and growth rates. A transcription of his paper, which appeared in the Proceedings of the London Mathematical Society in 1893, is included in the readme file. In 1979, N. J. Zabusky, M. H. Hughes and K. V. Roberts introduced a numerical scheme now commonly known as “Contour Dynamics.” This has been a popular tool for simulation of inviscid discrete patches of vorticity. It is numerically efficient because following the evolution of a uniform vorticity region only requires the tracking of its boundary. We implemented the contour dynamics algorithm in Matlab in order to re-examine the evolution of the Kirchhoff vortex, with an emphasis on the modes of the system. Two fitting routines are included which decompose the solutions into constituent linear eigenmodes. Some results from these routines will appear in Physics of Fluids in April 2008, and a preprint of this paper is also included in the readme file.
Acknowledgements	The author wishes to acknowledge the following in the creation of this submission: curvspace, Fast and Robust Curve Intersections, nearestneighbour.m
Required Products	Optimization Toolbox
MATLAB release	MATLAB 7.1.0 (R14SP3)
Zip File Content
Other Files	Kirchhoff Vortex Contour Dynamics Simulation/CalcLinEvolution.m, Kirchhoff Vortex Contour Dynamics Simulation/CalcPertAreaChange.m, Kirchhoff Vortex Contour Dynamics Simulation/ControlString.m, Kirchhoff Vortex Contour Dynamics Simulation/curvspace.m, Kirchhoff Vortex Contour Dynamics Simulation/dZdt.m, Kirchhoff Vortex Contour Dynamics Simulation/ellipsefit.m, Kirchhoff Vortex Contour Dynamics Simulation/FitLoveEnd.m, Kirchhoff Vortex Contour Dynamics Simulation/FitString.m, Kirchhoff Vortex Contour Dynamics Simulation/intersections.m, Kirchhoff Vortex Contour Dynamics Simulation/Kirchhoff_CD_Simulation.m, Kirchhoff Vortex Contour Dynamics Simulation/LoadAscii.m, Kirchhoff Vortex Contour Dynamics Simulation/LoadExpData.m, Kirchhoff Vortex Contour Dynamics Simulation/LoveLinearFit.m, Kirchhoff Vortex Contour Dynamics Simulation/LoveNonLinearFit.m, Kirchhoff Vortex Contour Dynamics Simulation/nearestneighbour.m, Kirchhoff Vortex Contour Dynamics Simulation/PiecewiseIntegration.m, Kirchhoff Vortex Contour Dynamics Simulation/ReadAndPlotResults.m, Kirchhoff Vortex Contour Dynamics Simulation/ReadMe.pdf, Kirchhoff Vortex Contour Dynamics Simulation/ScanParameters.m

Tags for This File
Everyone's Tags	chemistry, kirchhoff vortex contour dynamics 2d fluids ellipse elliptical, physics
Tags I've Applied
Add New Tags	Please login to tag files.

Please login to add a comment or rating.

Updates
31 Mar 2008	Title was garbled (repeated twice)

Tag Activity for this File
Tag	Applied By	Date/Time
chemistry	Travis Mitchell	22 Oct 2008 09:54:43
physics	Travis Mitchell	22 Oct 2008 09:54:43
kirchhoff vortex contour dynamics 2d fluids ellipse elliptical	Travis Mitchell	22 Oct 2008 09:54:43

MATLAB Central Terms of Use

NOTICE: Any content you submit to MATLAB Central, including personal information, is not subject to the protections which may be afforded information collected under other sections of The MathWorks, Inc. Web site. You are entirely responsible for all content that you upload, post, e-mail, transmit or otherwise make available via MATLAB Central. The MathWorks does not control the content posted by visitors to MATLAB Central and, does not guarantee the accuracy, integrity, or quality of such content. Under no circumstances will The MathWorks be liable in any way for any content not authored by The MathWorks, or any loss or damage of any kind incurred as a result of the use of any content posted, e-mailed, transmitted or otherwise made available via MATLAB Central. Read the complete Terms prior to use.