  We present here a series of numerical simulations of the development of
Kelvin-Helmholtz instability in a relativistically hot plasma. The physical
parameters in the unperturbed state are chosen to be representative of local
conditions encountered in Pulsar Wind Nebulae (PWNe), with a main magnetic
field perpendicular to a mildly relativistic shear layers. By using a numerical
code for Relativistic MHD, we investigate the effect of an additional magnetic
field component aligned with the shear velocity, and we follow the evolution of
the instability to the saturation and turbulent regimes. Based on the resulting
flow structure, we then compute synchrotron maps in order to evaluate the
signature of Kelvin-Helmholtz instability on the emission and we investigate
how the time scale and the amplitude of the synchrotron modulations depend on
shear velocity and magnetic field. Finally we compare our results to the
observed variable features in the Crab Nebula. We show that the
Kelvin-Helmholtz instability cannot account for the wisps variability, but it
might be responsible for the time dependent filamentary structure observed in
the main torus.
