  We derive analytically the vorticity generated downstream of a
two-dimensional rippled hydromagnetic shock neglecting fluid viscosity and
resistivity. The growth of the turbulent component of the downstream magnetic
field is driven by the vortical eddies motion. 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 field
lines whirling. The explicit expression of the amplification growth rate and of
the non-linear field back-reaction in terms of the parameters of shock and
interstellar density fluctuations is derived from MHD jump conditions at
rippled shocks. A magnetic field saturation up to the order of milligauss and a
short-time variability in the $X$-ray observations of supernova remnants can be
obtained by using reasonable parameters for the interstellar turbulence.
