  In this visualisation the instantaneous local velocity is expressed in terms
of four components to capture the development of and interactions between
coherent structures in turbulent flows. It is then possible to isolate the
terms linked with each major type of structure and identify the corresponding
subsets of the Navier-Stokes equations that are easier to solve than the full
version. Each of these subsets applies to a domain in the flow field not a flow
regime. The traditional statistics of turbulence are shown to be not specific
to turbulent flow. In particular the Reynolds stresses, the probability density
function, the dissipation, the production and the energy spectrum are obtained
from one subset associated with unsteady "laminar" flow. The evidence also
indicates that the Kolmogorov scale does not represent an eddy size and more
importantly that it does not require the assumption of local isotropy.
Applications of this visualisation include a proposal for a theoretical closure
of the Reynolds equations, the collapse of velocity and skin friction profiles
for Newtonian and non-Newtonian fluid flows in all geometries into unique
master curves. A new partial derivative is introduced that decouples the effect
of diffusion and convection simplifying the mathematical solution of subsets of
the NS equations with implications for a more efficient generation of
computational fluid dynamics packages. Finally the consequences to turbulent
heat and mass transfer are examined.
