Direct numerical testing of stationary shock model with low Mach number shock observations Academic Article uri icon


  • Almost all existing models of collisionless shocks, starting with the one-fluid MHD models and ending with the attempts of kinetic modeling of the shock front, are based on the two assumptions of the shock one-dimensionality and time station- arity. That means that all fields and hydrodynamical variables within the shock front depend only on the single coordinate along the shock normal and do not depend on time, at least at the typical ion timescale. Theoretical and observational descriptions, which use these assumptions, consider only some average profiles of the shock and do not take into account any rippling of the shock surface itself or waves and turbulence inside the shock front. The two assumptions are essential for both theoretical and observational shock physics. The very derivation of the Rankine-Hugoniot relations, connecting the upstream incident plasma parameters to downstream heated plasma parameters, requires one-dimensionality and time- stationarity. Theoretical expressions for the field profiles, in particular, for the cross-shock electric field (Scudder, 1995) and for the noncoplanar component of the magnetic field in the front of the quasi-perpendicular shock (Jones and Ellison, 1987, 1991; Gedalin, 1996a), are derived from two fluid hydrodynamics with the necessary implementation of the above assumptions. The description of ion motion and evolution of the ion distribution across the shock, including ion reflection and transmission, as governed by the static electromagnetic fields in the shock front, have been used for the explanation of the magnetic foot and overshoot formation at the supercritical shocks. The estimate of the foot length, which is widely used for the shock velocity determination, also exploits the shock one-dimensionality and stationarity (see, e.g., Sckopke et al., 1983, and references therein). Although this shock stationarity and one-dimensionality is taken for granted by theoreticians for model developments

publication date

  • January 1, 1998