This thesis aims to a better understanding of the crossing of the jet-stream from its warm side to its cold side by a number of mid-latitude winter storms. Indeed, these storms were observed to experiment an explosive growth phase just after the crossing, which justifies the importance of the crossing issue. We investigate how the inhomogeneous spatial structure of the large-scale jet-stream affects, beyond baroclinic instability, the trajectory and the deepening of surface depressions during the jet crossing. First we study, in a barotropic numerical idealized context, how the large-scale deformation effects modulate the meridional displacement of a cyclonic eddy. This displacement is primarily due to the nonlinear effect of the meridional gradient of the large-scale potential vorticity gradient (called beta-drift, known in the context of tropical cyclones and ocean eddies). It is shown that the deformation effects reinforce the anticyclone created by the Rossby wave radiation due to the potential vorticity gradient, and with which the cyclonic eddy interacts. Then this mechanism is generalized to a baroclinic atmosphere by studying the crossing by a cyclonic surface eddy of a meandering and baroclinically unstable jet-stream, within a two-layer model. It is shown that a positive barotropic potential vorticity gradient induces a strong altitude anticyclone which is responsible for the crossing of the jet by the surface eddy with which it interacts. In addition, the energetic life cycle of an idealized eddy undergoing the deformation effects appears to be similar to those of some real storms, including intensification just after jet crossing.
