  In this paper we analyze the transport of passive tracers by deterministic
stationary incompressible flows which can be decomposed over an infinite number
of spatial scales without separation between them. It appears that a low order
dynamical system related to local Peclet numbers can be extracted from these
flows and it controls their transport properties. Its analysis shows that these
flows are strongly self-averaging and super-diffusive: the delay $\tau(r)$ for
any finite number of passive tracers initially close to separate till a
distance $r$ is almost surely anomalously fast ($\tau(r)\sim r^{2-\nu}$, with
$\nu>0$). This strong self-averaging property is such that the dissipative
power of the flow compensates its convective power at every scale. However as
the circulation increase in the eddies the transport behavior of the flow may
(discontinuously) bifurcate and become ruled by deterministic chaos: the
self-averaging property collapses and advection dominates dissipation. When the
flow is anisotropic a new formula describing turbulent conductivity is
identified.
