Kelvin-Helmholtz multi-spacecraft studies at the Earth's magnetopause boundaries

The Kelvin-Helmholtz (KH) instability can operate in various situations in the solar wind, but at the boundaries of planetary obstacles, for example the Earth's magnetopause, it is most amenable to investigation. Reliable estimates of wave characteristics are essential for comparison with theoretical and numerical models and for understanding the non-linear development of KH waves and their role in the plasma entry into the magnetosphere. After discussing their typical conditions of appearance in KH unstable domains at the magnetopause, both theoretically and observationally, we outline recent results of multi-spacecraft analysis with Cluster giving accurate, albeit spatially limited, determination of surface wave characteristics. Those characteristics (wavelength and propagation direction), close to the terminator on the nightside, are likely to be prescribed by the 3-D geometry and the bending of field lines developed by the KH waves, rather than by the magnitude and the direction of the magnetosheath or background flow. An unprecedented number of satellites provides now the opportunity to extend the analysis of source regions of KH waves and their domains of development