Kelvin-Helmholtz instability at the magnetopause: theory and observations

The interaction between the solar wind and the Earth’s magnetosphere is mediated by the magnetopause. The dynamics occurring at this boundary depends on various aspects as, e.g., the solar wind dynamic pressure or the direction of the Interplanetary Magnetic Field (IMF). The solar wind, streaming from the Sun carries with it the IMF which interacts with northwards geomagnetic field lines causing magnetic reconnection events, particularly effective when the IMF is directed southwards. Magnetic reconnection makes a large amount of solar wind particles to be tranferred into the Earth’s magnetosphere. If the IMF is directed northward magnetic reconnection can take place at high latitude, but it is not efficient enough to justify the amount of cold and dense solar wind plasma observed by satellites inside the magnetosphere. Furthermore, in northwards conditions one observe the formation of a wide boundary layer at the low latitude. This boundary layer is thought to be the result of the observed plasma transfer driven by the development of the Kelvin-Helmholtz (K-H) instability. This instability, originating from the velocity shear between the solar wind and the almost static near-Earth plasma, develops along the flanks of the magnetopause giving rise to vortex like structures that in turn create the favorable conditions for solar wind plasma transfer. In particular, the vortices can merge forming eventually large structures, carrying with them solar wind plasma and magnetic field lines. The large scale dynamics of K-H vortices generates favorable conditions for the development of secondary instabilities important for the plasma transport as, for example Rayleigh-Taylor and secondary K-H instability, as well as magnetic reconnection occurring inside the vortices themselves or in-between. Numerical simulations have also shown that the long time evolution of this instability is characterized by the formation of a layer dominated either by vortex like, coherent structures or by small scale structures in a more or less turbulent state, depending on the competition between vortex pairing and secondary instabilities that take place in the non linear phase. In particular, last ten years of simulations have shown that the competition between the merging mechanism and the development of secondary instabilities depends strongly on the initial velocity, density and magnetic large scale field profiles used as initial conditions in the simulations. Therefore, in order to make a further step towards the comprehension of this complex system, it is imperative to combine satellite data and numerical simulations. The idea here is to initialize numerical simulations by using direct in-situ observations of the main field profiles since only a correct initialization can reproduce the correct dynamics. Note that in-situ measurements are limited at short crossings of the magnetopause for orbital reasons, so that we would not be able to follow the temporal evolution of the Kelvin-Helmholtz instability. The main goals of this thesis are: (i) to investigate the properties of the development of the K-H and its further non-linear dynamics eventually leading to turbulence; (ii) to investigate the small scale mechanisms occurring inside the mixing layer in the long time evolution of the instability; (iii) to find observational events when satellites cross the magnetopause under K-H condition but before the instability develops and (iv) to recover the profiles of the principal physical quantities and to use them to initialize our numerical simulations. In this study a “two-fluid” plasma model is adopted using 2D simulations to understand the role of K-H instability at low latitude magnetopause. The code has been developed at the University of Pise and has already been used for different scientific publications. From the experimental point of view, we use data from the ACE satellite orbiting in the solar wind to monitor the IMF conditions and the measurement from Cluster and Geotail satellites to study the magnetopause. In particular we use particles and electromagnetic fields to reconstruct the profiles across the magnetopause (density, magnetic and velocity fields profiles, etc..) to be used as more realistic initial conditions for the numerical simulations. The main results achieved during this work are: (i) characterize the turbulence inside K-H vortices and the small scale magnetic reconnection events responsible for the observed intermittency; (ii) select one event in particular where we have the combination of a satellite measurement before and after K-H develops and find that the density and velocity profile centers are shifted by a distance comparable to their shear lengths and (iii) that this initial shift cause a different evolution of the K-H instability leading to a final state in agreement with satellites observations. This thesis shows that the combination of spacecraft data and numerical simulations is the most effective way to study complex phenomenaof plasma transport across frontiers.