Concerning a problem on the Kelvin-Helmholtz stability of the thin magnetopause
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: (ρ0,1ρ0,2)(Vequation image,1 − Vequation image,2)2 < (4π)−1(ρ0,1 + ρ0,2)[(Bequation image,1)2 + (Bequation image,2)2] (a). Here the indices 1 and 2 refer to quantities on either side of the magnetopause, ρ0 is the plasma density, and Vequation image, Bκ are the projections of the plasma velocity equation image and magnetic field equation image on the direction of the wave vector equation image, 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 ρ0, equation image, and equation image, 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.
JGR: Space Physics
Digital Object Identifier (DOI)
Gratton, FT; Bender, L; Farrugia, CJ; Gnavi, G (2004). Concerning a problem on the Kelvin-Helmholtz stability of the thin magnetopause, JOURNAL OF GEOPHYSICAL RESEARCH-SPACE PHYSICS. Vol. 109, No. A4. DOI: 10.1029/2003JA010146