  Scaling and structural evolutions are contemplated in a new perspective for
turbulent channel flows. The total integrated turbulence kinetic energy remains
constant when normalized by the friction velocity squared, while the total
dissipation increases linearly with respect to the Reynolds number. This serves
as a global constraint on the turbulence structure. Motivated by the flux
balances in the root turbulence variables, we also discover dissipative scaling
for u2 and v2, respectively through its first and second gradients. This
self-similarity allows for profile reconstructions at any Reynolds numbers
based on a common template, through a simple multiplicative operation. Using
these scaled variables in the Lagrangian transport equation derives the
Reynolds shear stress, which in turn computes the mean velocity profile. The
self-similarities along with the transport equations render possible succinct
views of the turbulence dynamics and computability of the full structure in
channel flows.
