Hysteresis Model of a Nonstationary Shock

Previous analysis of two-spacecraft measurements as well as new Cluster observations show that at least some quasiperpendicular collisionless shocks are nonstationary. We present a simple hydrodynamic model with the diffusion which has the features resembling the time-dependent behavior of the shock front. The diffusion may be driven by current instabilities in the steep shock front, and is assumed to have a hysteresis behavior: it is switched on above some threshold (field gradient) during the steepening and switched off below lower threshold during unsteepening. An overshoot naturally appears during the shock formation. The shock is weakly nonstationary and oscillates around some average profile.