  Using the Lagrangian transport of momentum, the Reynolds stress can be
expressed in terms of basic turbulence parameters. The Reynolds stress gradient
represents the lateral transport of stream-wise momentum, balanced by the u2
transport, pressure and shear force terms in the momentum equation. Data from
direct numerical simulations (DNS) have been used to validate this approach,
with a good degree of consistency and agreement. This expression for the
Reynolds stress gradient adds a transport equation to the Reynolds-averaged
Navier-Stokes (RANS) equation, so that the turbulence structure can be
determined if the third unknown variable, u2, can be determined. Here, we
consider alternative structure-based methods for reconstruction of u2 profiles
for wall-bounded flows. The input of u2 profile, in conjunction with the two
transport equations (RANS and the current Reynolds stress equation), allows for
full reconstruction of the turbulent structure in wall-bounded flows, with
reasonable agreement with DNS data.
