Which Kelvin-Helmholtz waves grow along the spatially-varying magnetopause flanks and why?
By Harley Kelly (Imperial College London)
The Kelvin-Helmholtz instability mediates the viscous-like solar-terrestrial interaction, allowing solar wind plasma and energy to penetrate our magnetic shield through generating magnetopause surface waves that quickly become non-linear. Determining when and where this should occur and which wave modes grow has remained challenging. This is because the underlying theory has concentrated on local wave growth, where the locally most-unstable linear wave dominates. However, these waves travel along the boundary into new regions where the instability is still able to amplify these perturbations despite the different background properties. Two possible paradigms exist, waves are either:
(a) locally generated, being those predicted by the simple theory
(b) originate further upstream, having travelled and grown along the way
We address this conundrum by applying a machine learning technique, Dynamic Mode Decomposition, that efficiently extracts distinct wave modes from a simulation of the entire magnetosphere. This shows Kelvin-Helmholtz waves do grow quickly out of some points on the boundary, signaling local generation. However, their energy persists as they travel down the tail, slowly growing in both amplitude and spatial extent in the process due to the accelerating flow around the magnetosphere and its effect on the instability. Therefore, both effects play a role in which waves are dominant at any point.
These results may explain why longer wavelengths are observed in the tail than local theory predicts and motivates further exploration of tangential inhomogeneities in basic Kelvin-Helmholtz theory. We also highlight that Dynamic Mode Decomposition may prove a powerful technique for studying other forms of waves, instabilities and turbulence across the heliosphere.
See publication for more details:
Kelly, H. M., Archer, M. O., Eastwood, J. P., Heyns, M., Eggington, J. W. B. and Chittenden, J. P (2026). Superposition of Doppler-Shifting Magnetopause Kelvin-Helmholtz Modes Through Dynamic Mode Decomposition of a Global MHD Simulation. Geophysical Research Letters, 53, e2025GL120284, https://doi.org/10.1029/2025GL120284

Comparison of dynamic mode decomposition modes along equatorial magnetopause tangent showing (a) integrated energy densities and (b) polynomial-fit wavelengths. (c) Cartoon depicting key results.