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

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.