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 we present the results of a long time calculation. 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. We numerically study some aspects of the dependence of the solution on the initial condition and find agreement with Moore's asymptotic relation between the initial amplitude and the critical time. For large initial amplitudes, two cusps form in the sheet strength, corresponding to double roll up. We explain why the Poincare recurrenc theorem does not imply that the sheet will eventually unroll. Our results suggest that beyond the critical time, the vortex sheet becomes a spiral with infinite arclength although we have doubts about the approximation's accuracy in that regime. 36 references, 30 figures, 3 tables.
- Research Organization:
- Lawrence Berkeley Lab., CA (USA)
- DOE Contract Number:
- AC03-76SF00098
- OSTI ID:
- 5309899
- Report Number(s):
- LBL-17092; ON: DE84006613
- Resource Relation:
- Other Information: 1, Thesis
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
VORTEX FLOW
HELMHOLTZ INSTABILITY
ANALYTICAL SOLUTION
FLUID MECHANICS
FOURIER ANALYSIS
LEAST SQUARE FIT
NUMERICAL SOLUTION
SPIRAL CONFIGURATION
THEORETICAL DATA
CONFIGURATION
DATA
FLUID FLOW
INFORMATION
INSTABILITY
MAXIMUM-LIKELIHOOD FIT
MECHANICS
NUMERICAL DATA
PLASMA INSTABILITY
PLASMA MACROINSTABILITIES
640410* - Fluid Physics- General Fluid Dynamics