Compressible Kelvin-Helmholtz instability at the terrestrial magnetopause

González, Antonio Bueno; Gratton, Julio; Gratton, F. T.; Farrugia, Charles J.

doi:10.1590/s0103-97332002000500021

Cited by 9 publications

(12 citation statements)

References 18 publications

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“…Ordinarily, the secondary modes have growth rates smaller than those of the main branch [ González and Gratton , 1994]. In contrast, compressibility effects become very important, also for the main branch of the KH instability, at the supersonic flows that are encountered at the magnetospheric flanks [ González et al , 2002]. Thus the present analysis is restricted to the dayside magnetopause.…”

Section: Kelvin‐helmholtz Instability For a Smooth Transitionmentioning

confidence: 99%

Concerning a problem on the Kelvin‐Helmholtz stability of the thin magnetopause

et al. 2004

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[1] According to incompressible MHD theory, when the magnetopause is modeled as a tangential discontinuity with jumps in the field and flow parameters, it is KelvinHelmholtz (KH) stable when the following inequality is satisfied: (r 0,1 r 0,2 )(Here the indices 1 and 2 refer to quantities on either side of the magnetopause, r 0 is the plasma density, and V k , B k are the projections of the plasma velocity V 0 ! and magnetic field B 0 ! on the direction of the wave vector k ! , respectively. An example of a continuous velocity profile with finite thickness D 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 D ! 0. Using hyperbolic tangent profiles for r 0 , V 0 ! , and B 0 ! , 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.INDEX TERMS: 2752 Magnetospheric Physics: MHD waves and instabilities; 2724 Magnetospheric Physics: Magnetopause, cusp, and boundary layers; 2784 Magnetospheric Physics: Solar wind/magnetosphere interactions; 3230 Mathematical Geophysics: Numerical solutions; KEYWORDS: Kelvin-Helmholtz instability, magnetopause instability, low magnetic shear bands at the frontside magnetopause, tangential discontinuity stability criterion

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Section: Kelvin‐helmholtz Instability For a Smooth Transitionmentioning

confidence: 99%

Concerning a problem on the Kelvin‐Helmholtz stability of the thin magnetopause

et al. 2004

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“…Less well‐known is the fact that in a compressible plasma there can be two KH unstable often distinct flow speed regions, which allow for the existence of a primary as well as a less intense secondary KHI interval, depending on the ambient plasma parameters [ González and Gratton , ; González et al , ; Taroyan and Erdélyi , , ]. This secondary instability region occurs for flow speeds typically below the primary KHI and with usually smaller growth rates.…”

Section: Introductionmentioning

confidence: 99%

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

2013

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Primary and secondary Kelvin‐Helmholtz surface wave modes on the Earth's magnetopause are studied within the framework of warm plasma ideal magnetohydrodynamics (MHD) across an infinitely thin magnetopause tangential discontinuity (TD). With the increase of background flow velocity, a Kelvin‐Helmholtz Instability (KHI) unstable boundary separating two uniform semi‐infinite plasma regions is always ultimately stabilized to KHI growth at an upper cut‐off while inclusion of an inner boundary in one plasma region removes this stabilization. Phase velocity Friedrichs diagrams are presented that allow us to identify unstable fast and slow modes that correspond to growing modes of the KHI under different magnetosphere and magnetosheath conditions. On the nightside magnetosphere, and the magnetotail, new KH unstable intermediate‐fast modes are created, which cannot propagate exactly perpendicular to the magnetic field. In the plasma frame, primary unstable KH waves show fast/fast, while secondary KH waves show slow/fast mode behavior in the magnetosphere/magnetosheath. Secondary KHI occurs at slower flow speeds than the primary KHI and grows more slowly and at a narrow range of propagation angles. Our analysis is placed in the context of in situ satellite observations of the phase speed of KHI‐related waves in the magnetosheath and magnetosphere in the long wavelength regime where our analysis applies. We conclude that KH unstable surface waves on the near‐Earth magnetopause flanks are likely to be secondary KHI waves, while those further down the flanks and on the nightside magnetopause are likely to be primary KHI waves—the latter being the most important for energy transport at the magnetopause.

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“…This was first hypothesised in 1955 by Dungey [20] and after which many studies were undertaken using incompressible simulations, but satellite observations suggested that the assumption of an incompressible flow is not accurate, thus much research into the compressible case has now been performed, whose results are confirmed by data collected by spacecraft such as the ISEE [21]. Later work by González et al [19] shows that an incompressible model can be used near the front of the magnetopause as the relative velocities across it are lower, but further down the magnetopause compressibility needs to be taken into account. The effects on the formation of the KHI in a compressible flow, as opposed to in an incompressible flow, are: a lower critical relative velocity across the shear layer before the onset of the instability, and reduced growth rate of the instability [19,21].…”

Section: Kelvin-helmholtz Instabilitymentioning

confidence: 99%

Kelvin-Helmholtz Instability on the Mach Reflection Shear Layer

Rubidge

Skews

Paton

et al. 2015

29th International Symposium on Shock Waves 2

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The Kelvin-Helmholtz Instability (KHI) is an instability that takes the form of repeating wave like structures. It forms on a shear layer where two fluids are moving at a relative velocity to one another. Such a shear layer forms as part of the Mach reflection. This dissertation focuses on experimentally visualising the presence of the KHI on the Mach reflection shear layer, as well as its evolution. Experimentation was performed at Mach numbers of 1.34, 1.46 and 1.61. Plain and parabolic entrance test pieces with varying wedge angles of 30 • to 38 • were tested. Flow field visualisation was performed with a schlieren optical system. The cameraside knife edge orientation was altered to vary the axis of sensitivity of the optical system. It was found that the KHI did form on the Mach reflection shear layer; more readily with increasing Mach number and wedge angle. The evolution of the instability was found to be almost scalable, with M 0 = 1.46 and M 0 = 1.61 achieving the best scaling of the length and average width of the KHI respectively. The KHI was best visualised with the camera-side knife edge perpendicular to the shear layer (i.e. the axis of sensitivity along the length of the shear layer), the visualisation of the KHI was completely obscured when camera-side knife edge was parallel to the shear layer. Second order Euler, Navier-Stokes and k-ǫ numerical simulations of the flow field were also conducted using FLUENT 13. It was found that the Euler and Navier-Stokes solvers achieved very similar results, both producing the KHI but at a much less developed state than the experimental cases. The k-ǫ solver, however, did not produce the KHI.

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Compressible Kelvin-Helmholtz instability at the terrestrial magnetopause

Cited by 9 publications

References 18 publications

Concerning a problem on the Kelvin‐Helmholtz stability of the thin magnetopause

Concerning a problem on the Kelvin‐Helmholtz stability of the thin magnetopause

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

Kelvin-Helmholtz Instability on the Mach Reflection Shear Layer

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