A generic model for advection. of a scalar by E x B flow with a linearly va
rying mean shows that the cross phase factor in the transport flux is stron
gly reduced in the strong shear regime (shearing rate > eddy turnover rate)
, leading to significant transport suppression. The cross phase scales much
more strongly with shear strength than do fluctuation amplitudes, allowing
significant transport reduction even if fluctuations increase, or decrease
only slightly. Cross-phase suppression thus can be the dominant transport-
reduction mechanism in transport barriers.