  In this letter we report on turbulent acceleration of the dissipation of
magnetic field in the postshock re- gion of a Poynting flux-dominated flow,
such as the Crab pulsar wind nebula. We have performed two- dimensional
resistive relativistic magnetohydrodynamics simulations of subsonic turbulence
driven by the Richtmyer-Meshkov instability at the shock fronts of the Poynting
flux-dominated flows in pulsar winds. We find that turbulence stretches current
sheets which substantially enhances the dissipation of magnetic field, and that
most of the initial magnetic field energy is dissipated within a few
eddy-turnover times. We also develop a simple analytical model for turbulent
dissipation of magnetic field that agrees well with our simulations. The
analytical model indicates that the dissipation rate does not depend on
resistivity even in the small resistivity limit. Our findings can possibly
alleviate the {\sigma}-problem in the Crab pulsar wind nebulae.
