Kelvin-Helmholtz Waves Magnetic Curvature and Vorticity: Four-Spacecraft Cluster Observations

[1] Magnetopause Kelvin-Helmholtz (KH) waves are rich in complex magnetic and flow structures which are key to understand the role of these waves in facilitating the solar wind plasma transport into the Earth's magnetosphere. Four spacecraft in tetrahedral configuration provide the tools necessary for characterizing in situ magnetic geometry and vortical flow. We apply the tools on KH waves observed by Cluster inside an electron boundary layer on the duskside magnetopause. Magnetic curvature and flow vorticity properties of the KH waves are obtained for various solar wind conditions. Smaller curvature radius and higher-positive vorticity are found for longer wavelength. Changes in KH wavelengths observed with relatively fixed tetrahedron size allow us to resolve magnetic curvature in multiscales. For the first time in a space plasma, we report the dependence of the curvature radius measurement on the ratio of the tetrahedron size to the wavelength, consistent with nonlinear spatial variations of magnetic structures that would be resolved by nested cross-scale spacecraft tetrahedrons. Negative vorticity is found to develop in the rolled-up vortex, adjacent to positive vorticity in the vortex core. The strength of negative vorticity is found to increase with the solar wind proton density and proton bulk flow speed. This study provides observational evidence of multiscale magnetic structures and is useful for understanding the development of rolled-up vortex signatures during various stages of solar wind-controlled KH wave evolution.