Formation and identification of Kelvin-Helmholtz generated vortices at Earths magnetopause: Insight from adapting hydrodynamic techniques for MHD

The Kelvin-Helmholtz Instability (KHI) plays a significant role in the viscous-like mass, momentum, and energy transfer from the solar wind into the magnetosphere through both vortical and wave dynamics. To confidently study and compare the effects of these dynamics, we must formally define a vortex. Previously, a definition did not exist for the magnetohydrodynamic (MHD) regime. Consequently, we have developed a novel vortex definition (the `λ_MHD definition’) for MHD flows. This is based on adapting well-used hydrodynamic techniques (the λ₂ family of methods) that defines a vortex as a local minimum in an adapted pressure field. We derive the MHD suitable adapted pressure field from the ideal MHD Cauchy-Momentum equation, and find that it is composed of four components. The first three components represent the hydrodynamic properties of rotational momentum flow, density inhomogeneity, and fluid compressibility respectively. The final component makes the λ_MHD definition unique from hydrodynamics as it represents the rotational component of the J×B Lorentz force which is found using a Helmholtz decomposition. We use the Gorgon global 3-Dimensional MHD code to validate the λ_MHD vortex definition within a northward IMF simulation run exhibiting KHI-driven waves at the magnetopause flanks. Comparison of λ_MHD with existing hydrodynamic definitions shows good correlations and skill scores, particularly with the more advanced methods. Our analysis also reveals that the rotational momentum flow term dominates at the magnetopause. The other components provide typically small corrections to this. We have found that at the magnetopause, compressibility generally acts in opposition to the existence of a pressure minimum and thus a vortex. Alternatively, inhomogeneity and the rotational component of the Lorentz force generally act to support the pressure minimum. We explore potential physical reasons for these results and discuss potential applications of this method to further simulation and spacecraft observations.