Numerical study of Kelvin-Helmholtz instability by the point vortex method
Rosenhead's classical point vortex numerical method for studying the evolution of a vortex sheet from analytic initial data (Kelvin-Helmholtz instability) is examined using the discrete Fourier analysis techniques of Sulem, Sulem and Frisch. One cause for the chaotic motion previously observed in computations using a large number of vortices is that short wavelength perturbations are introduced spuriously by finite precision arithmetic and become amplified by the model's dynamics. Methods for controlling this source of error are given, and the results confirm the formation of a singularity in a finite time which was previously found by Moore and Meiron, Baker and Orszag using different techniques of analysis. A cusp forms in the vortex sheet strength at the critical time, explaining the onset of erratic particle motion in applications of the numerical methods of Van de Vooren and Fink and Soh to this problem. Unlike those methods, the point vortex approximation remains consistent at the critical time and results of a long time calculation are presented. The singularity is interpreted physically as a discontinuity in the strain rate along the vortex sheet and also as the start of roll up on a small scale. The author numerically studies some aspects of the dependence of the solution on the initial condition and finds agreement with Moore's asymptotic relation between the initial amplitude and the critial time.
- Research Organization:
- California Univ., Berkeley (USA)
- OSTI ID:
- 6022602
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
700105 -- Fusion Energy-- Plasma Research-- Plasma Kinetics-Theoretical-- (-1987)
700107* -- Fusion Energy-- Plasma Research-- Instabilities
EQUATIONS
FOURIER ANALYSIS
HELMHOLTZ INSTABILITY
INSTABILITY
KINETIC EQUATIONS
NUMERICAL SOLUTION
PARTICLE KINEMATICS
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES