Kelvin-Helmholtz instability of a phased-mixed Alfven wave

Details Kelvin-Helmholtz instability of a phased-mixed Alfven wave Kelvin-Helmholtz instability of a phased-mixed Alfven wave

Feb 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984a%26a...131..283b&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 131, no. 2, Feb. 1984, p. 283-290. Research supported by the Science and Engin

Astronomy and Astrophysics

Astrophysics

38

Kelvin-Helmholtz Instability, Magnetohydrodynamic Waves, Plasma Heating, Solar Corona, Hydrodynamic Equations, Mixing, Velocity Distribution

Scientific paper

The development of the Kelvin-Helmholtz instability at the velocity antinodes of a standing Alfven wave is studied. The problem is investigated at large times, when the velocity profile has a sinusoidal form, and at the onset of instability. At large times it is found that the growth rates of the sinusoidal profile are much smaller, and that the most unstable wavelengths are about 12 times the phase-mixed velocity inhomogeneity length scale, whereas for the square wave, short waves are the most unstable. In a temporally local stability analysis, a critical time is found after which the instability grows significantly within one Alfven wave period. This critical time is related to the dimensionless wave frequency Omega1 = (k-parallel)(a)/M, where k-parallel is the Alfven wavenumber and M is the magnetic Mach number. The growth rate of the instability is determined as a function of time for several values of Omega1, and the critical time is found at which the growth rate is equal to the wave frequency. It is shown that the instability develops within very few wave periods, thus it is expected that a shear Alfven wave would rapidly be disrupted by Kelvin-Helmholtz instability.

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