  Tangled magnetic fields, often coexisting with an ordered mean field, have a
major impact on turbulence and momentum transport in many plasmas, including
those found in the solar tachocline and magnetic confinement devices. We
present a novel mean field theory of potential vorticity mixing in
$\beta$-plane magnetohydrodynamic (MHD) and drift wave turbulence. Our results
show that mean-square stochastic fields strongly reduce Reynolds stress
coherence. This decoherence of potential vorticity flux due to stochastic field
scattering leads to suppression of momentum transport and zonal flow formation.
A simple calculation suggests that the breaking of the shear-eddy tilting
feedback loop by stochastic fields is the key underlying physics mechanism. A
dimensionless parameter that quantifies the increment in power threshold is
identified and used to assess the impact of stochastic field on the L-H
transition. We discuss a model of stochastic fields as a resisto-elastic
network.
