Open AccessConcerning a problem on the Kelvin‐Helmholtz stability of the thin magnetopause
Author(s) -
Gratton Fausto T.,
Bender Laurence,
Farrugia Charles J.,
Gnavi Graciela
Publication year - 2004
Publication title -
journal of geophysical research: space physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.67
H-Index - 298
eISSN - 2156-2202
pISSN - 0148-0227
DOI - 10.1029/2003ja010146
Subject(s) - magnetopause , physics , magnetohydrodynamics , mathematical analysis , magnetosheath , helmholtz free energy , stability (learning theory) , magnetic field , classical mechanics , compressibility , mechanics , geophysics , mathematics , solar wind , quantum mechanics , machine learning , computer science
According to incompressible MHD theory, when the magnetopause is modeled as a tangential discontinuity with jumps in the field and flow parameters, it is Kelvin‐Helmholtz (KH) stable when the following inequality is satisfied: (ρ 0,1 ρ 0,2 )( V ,1 − V ,2) 2 < (4π) −1 (ρ 0,1 + ρ 0,2 )[( B ,1) 2 + ( B ,2) 2 ] ( a ). Here the indices 1 and 2 refer to quantities on either side of the magnetopause, ρ 0 is the plasma density, and V , B κ are the projections of the plasma velocity and magnetic field on the direction of the wave vector , respectively. An example of a continuous velocity profile with finite thickness Δ that can be solved in closed form is presented for which condition ( a ) is satisfied. Yet the configuration can be shown to be KH unstable, and it approaches stability only in the limit Δ → 0. Using hyperbolic tangent profiles for ρ 0 , , and , and solving the stability problem numerically with parameters typical of the dayside magnetopause, we show cases of unstable configurations, all of which are stable according to ( a ). This possibility, as far as we know, has passed unnoticed in the literature. Being incompressible, the theory applies to subsonic regions of the dayside magnetopause. We conclude that condition ( a ) must be used with care in data analysis work.