On the kelvin-Helmholtz instability of the Earth's magnetopause

Abstract

The effect of the finite thickness of the shear layer on the Kelvin-Helmholtz instability of the Earth's magnetopause boundary is investigated. The thickness of the layer stabilizes the boundary with respect to short wavelength perturbations, which were previously found to be unstable in the zero thickness analysis. Compressibility effects further stabilize the layer. The effects of the magnetic field on the instability are also discussed.

A comparison of magnetohydrodynamic instabilities at the Martian ionopause

“…Near the equatorial flanks, we assume that the ionosphere composition is the same than near the terminator, but the magnetosheath conditions differ significantly from the values at the terminator (Penz et al, 2004). For a nominal solar wind velocity of 400 km/s, the flow velocity in the magnetosheath is 360 km/s, giving a maximum growth rate of 0.15 s À1 at wavelength slightly more than 100 km, which corresponds to a growth time of 7 s. For a low solar wind velocity, the maximum growth rate of 0.35 s À1 occurs for wavelength of about 40 km, which is not in agreement with the finite boundary condition by Ong and Roderick (1972), that the wave number k for the maximum instability growth rate must satisfy the condition ka/2 % 0.5, where a is the thickness of the boundary layer. For wavelength of 100 km, the growth rate is 0.2 s À1 and the growth time is 5 s.…”

Primary and secondary compressible Kelvin‐Helmholtz surface wave instabilities on the Earth's magnetopause

“…In the KHI studies, the magnetopause boundary is often assumed to have zero thickness [ Pu and Kivelson , , ; Mann et al , ; Mills et al , ; Mills and Wright , ]; this assumption is valid for waves with wavelengths bigger than the thickness of the boundary layer. Under this assumption, the growth rates of the KH unstable waves increase without limit as the tangential wave number increases [ Southwood , ; Ong and Roderick , ; Mann et al , ]. Study of KHI with the finite transition thickness was first done by Ong and Roderick [] employing both incompressible and compressible flow analysis.…”

On the predominance of oblique disturbances in the supersonic shear flow instability of the geomagnetic tail boundary

“…As follows from Eqs. (4)-(6) (see also Sen, 1964;Ong and Roderick, 1972), instead of the number M = u/c s , for characterizing the compressibility influence when B 0 = 0, one has to take the "magnetosonic Mach number":…”

“…Therefore, when, for analyzing the dispersion properties of the shear flow at the magnetospheric flanks, it is necessary to simultaneously take into account the influence of the following three factors, as follows: the density inhomogeneity, the magnetic field, and the compressibility. Such an analysis was never performed for the magnetopause instability (Sen, 1964;Parker, 1964;Moskvin and Frank-Kamenetsky, 1967;McKenzie, 1970;Ong and Roderick, 1972;Ershkovich and Nusinov, 1972;Southwood, 1979;Walker, 1981;Pu and Kivelson, 1983;Kivelson and Chen, 1995;Miura, 1982Miura, , 1990Miura, , 1992Miura, , 1996Miura, , 1999Farrugia et al, 2000). Apparently, this can distort results of a nonlinear modeling of the shear flow instability (Wu, 1986;Belmont and Chanteur, 1989;Miura, 1990Miura, , 1992Miura, , 1996Miura, , 1999Shen and Liu, 1999) as well as analysis results on the excitation of waveguide modes (Mann et al, 1999).…”