2013ApJ...770...84F

We analytically derive the vorticity generated downstream of a two-dimensional (2D) rippled hydromagnetic shock neglecting fluid viscosity and resistivity. The growth of the turbulent component of the downstream magnetic field is driven by the motion of vortical eddies. We determine an analytic time evolution of the magnetic field amplification at shocks, so far described only numerically, until saturation occurs due to seed-field reaction to the whirling of field lines. The explicit expression of the amplification growth rate and of the nonlinear field back-reaction in terms of the parameters of shock and interstellar density fluctuation is derived from MHD jump conditions at rippled shocks. A magnetic field saturation up to the order of milli-Gauss and a short-term variability in the X-ray observations of supernova remnants can be obtained by using reasonable parameters for the interstellar turbulence.