Superposition of Doppler-shifting magnetopause Kelvin-Helmholtz modes through Dynamic Mode Decomposition of a global MHD simulation

The Kelvin-Helmholtz instability mediates the viscous-like solar-terrestrial interaction by generating magnetopause surface waves that quickly become non-linear. Basic theory predicts the locally most-unstable linear wave dominates. However, Kelvin-Helmholtz is a broad, convective instability that also amplifies waves originating upstream. We address this conundrum by applying Dynamic Mode Decomposition to a Gorgon global magnetohydrodynamic simulation of the Kelvin-Helmholtz instability. While distinct modes quickly grow at points along the magnetopause, signalling local generation, their energy continues to slowly grow downtail. Thus, a superposition is present along the magnetopause, where the dominant mode is not always the locally fastest-growing. Each mode’s wavelength elongates downtail, correlating with the boundary layer flow speed due to the accelerating advective flow around the magnetosphere Doppler shifting the fixed-frequency waves. This may explain why longer wavelengths are observed in the tail than theory predicts and motivates further exploration of tangential inhomogeneities in basic Kelvin-Helmholtz theory.