  In this letter, we describe results of new high-resolution axisymmetric
relativistic MHD simulations of Pulsar Wind Nebulae. The simulations reveal
strong breakdown of the equatorial symmetry and highly variable structure of
the pulsar wind termination shock. The synthetic synchrotron maps, constructed
using a new more accurate approach, show striking similarity with the well
known images of the Crab Nebula obtained by Chandra, and the Hubble Space
Telescope. In addition to the jet-torus structure, these maps reproduce the
Crab's famous moving wisps whose speed and rateof production agree with the
observations. The variability is then analyzed using various statistical
methods, including the method of structure function and wavelet transform. The
results point towards the quasi-periodic behaviour with the periods of 1.5-3yr
and MHD turbulence on scales below 1yr. The full account of this study will be
presented in a follow up paper.
