  A simple analytical model for a turbulent flow is proposed, which considers
the flow as a collection of localized spatial structures that are composed of
elementary "cells" in which the state of the particles (atoms or molecules) is
uncertain. The Reynolds number is associated with the ratio between the total
phase volume for the system and that for the elementary cell. Calculating the
statistical weights of the collections of the localized structures, it is shown
that as the Reynolds number increases, the elementary cells group into the
localized structures, which successfully explains the onset of turbulence and
some other characteristic properties of turbulent flows. It is also shown that
the basic assumptions underlying the model are involved in the derivation of
the Navier-Stokes equation, which suggests that the driving force for the
turbulent transition described with the hydrodynamic equations is essentially
the same as in the present model, i.e. the tendency of the system to occupy a
statistically dominant state plays a key role. The instability of the flow can
then be a mechanism to initiate the structural rearrangement of the flow to
find this state.
