Self-consistent development of transport barriers is investigated analytically and numerically in flux driven interchange turbulence with highly intermittent turbulent fluxes. Numerical simulations on a bounded domain show turbulence leading to a homogenization of Lagrangian invariants by mixing, resulting in quasisteady pressure profiles predicted by turbulent equipartition. Below a critical aspect ratio alpha=L-y/L-x-for our parameters approximate to3.8-which is related to the rotational transform, large scale poloidal flows develop. They reduce the energy in the turbulence, prevent mixing, and constitute transport barriers for the turbulent fluxes, but are intermittently disrupted by strong bursts in the transport, which may be related to the strong edge localized modes observed in toroidal devices. (C) 2003 American Institute of Physics.