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

Abstract

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.

Emission of magnetosound from MHD‐unstable shear flow boundaries

“…Figure shows that the phase speed values of the KHI waves are in the expected range of fast MHD waves. This is consistent with the results of Turkakin et al [], where it is shown that the fastest growing KHI modes, i.e., primary KHI modes, are fast MHD waves.…”

“…Some studies have assumed a zero thickness boundary, which is appropriate if the wavelengths of the generated waves are significantly larger than the thickness of the boundary [ Pu and Kivelson , ; Mann et al , ; Turkakin et al , , ]. The effects of a finite boundary thickness have also been investigated in several studies [ Ong and Roderick , ; Walker , ; Farrugia et al , ; Contin et al , ; Gratton et al , ].…”

Kelvin-Helmholtz unstable magnetotail flow channels: Deceleration and radiation of MHD waves

“…We also calculated the phase velocities, , periods, T r =2π/ ω r , and the propagation angles with respect the background flow, β = tan − 1( k y / k x ) for these modes. Normalized phase velocities show that the primary kink and sausage modes are fast waves, while the secondary kink and sausage modes are slow waves in the stationary plasma frame in region 1 (not shown here) consistent with the results shown in Turkakin et al []. Variations of propagation angles, β , with background flow are displayed in Figure c and are found to vary between ≃0°–64°for primary and ≃0°–40°for secondary KHI waves.…”

“…The eigenfrequency variation with increasing normalized flow speed, V 02 = U 02 / V A 2 , in the channel is shown in Figures a and b, where both kink and sausage modes show two distinct K‐H unstable regions representing primary and secondary KHIs [c.f., Turkakin et al , ]. The secondary KHI becomes unstable at lower BBF flows, V 02 ≃2.8, than primary KHI, V 02 ≃3.3, which agrees with the results in Turkakin et al [].…”

“…Our results show that both slow and fast kink and sausage MHD waves may become KH unstable at sufficiently fast flow speeds, resulting in the primary and secondary KHIs, respectively [cf. Turkakin et al, 2013]. We further investigate the possibility that the KHI may cause the emission of MHD waves from the shear flow boundary in a similar manner to that suggested by Mann et al [1999] as applied to the magnetopause.…”