Abstract
For many years quasilinear renormalization has been applied to
numerous problems in turbulent transport. This scheme relies on
the localization hypothesis to derive a linear transport equation
from a simplified stochastic description of the underlying
microscopic dynamics. However, use of the localization hypothesis
narrows the range of transport behaviors that can be captured by
the renormalized equations. In this paper, we construct a
renormalization procedure that manages to avoid the localization
hypothesis completely and produces renormalized transport
equations, expressed in terms of fractional differential
operators, that exhibit much more of the transport phenomenology
observed in nature. This technique provides with a first step
towards establishing a rigorous link between the microscopic
physics of turbulence and the fractional transport models proposed
phenomenologically for a wide variety of turbulent systems such as
neutral fluids or plasmas.