  Using the Lagrangian transport of momentum, the Reynolds shear stress can be
expressed in terms of basic turbulence parameters. In this view, the Reynolds
stress gradient represents the lateral transport of streamwise momentum,
balanced by the u2 transport, pressure and shear force terms in the momentum
equation. We extend this formalism to other turbulence parameters such as
diagonal components of the Reynolds stress, and also to more complex flows
(boundary layer flows with adverse pressure gradients and pipe flows with
swirl). Data from direct numerical simulations (DNS) are used to validate this
full set of turbulent transport equations, exhibiting a good degree of
consistency and agreement for all of the components and across different
geometries. An example of the use of this full set of turbulence transport
equations is shown for turbulent jet flows.
