  There are two components in this work that allow solutions of the turbulent
channel problem: one is the Galilean-transformed Navier-Stokes equation which
gives a theoretical expression for the Reynolds stress; and the second the
maximum entropy principle which provides the spatial distribution of turbulent
kinetic energy. The first concept transforms the momentum balance for a control
volume moving at the local mean velocity, breaking the momentum exchange down
to its basic components. The Reynolds stress gradient budget confirms this
alternative interpretation of the turbulence momentum balance, as validated
with DNS data. The second concept of maximum entropy principle states that
turbulent kinetic energy in fully-developed flows will distribute itself until
the maximum entropy is attained while conforming to the physical constraints.
By equating the maximum entropy state with maximum allowable (viscous)
dissipation at a given Reynolds number, along with other constraints, we arrive
at function forms (inner and outer) for the turbulent kinetic energy. This
allows us to compute the Reynolds stress, then integrate it to obtain the
velocity profiles in channel flows. The results agree well with direct
numerical simulation (DNS) data at Re = 400 and 1000.
