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There are two components in this work that allow solutions of the turbulentchannel problem: one is the Galilean-transformed Navier-Stokes equation whichgives a theoretical expression for the Reynolds stress; and the second themaximum entropy principle which provides the spatial distribution of turbulentkinetic energy. The first concept transforms the momentum balance for a controlvolume moving at the local mean velocity, breaking the momentum exchange downto its basic components. The Reynolds stress gradient budget confirms thisalternative interpretation of the turbulence momentum balance, as validatedwith DNS data. The second concept of maximum entropy principle states thatturbulent kinetic energy in fully-developed flows will distribute itself untilthe 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 arriveat function forms (inner and outer) for the turbulent kinetic energy. Thisallows us to compute the Reynolds stress, then integrate it to obtain thevelocity profiles in channel flows. The results agree well with directnumerical simulation (DNS) data at Re = 400 and 1000.

Maximum Entropy Method for Solving the Turbulent Channel Flow Problem