Bulk flow scaling for turbulent channel and pipe flows

We report a theory deriving bulk flow scaling for canonical wall-bounded flows. The theory accounts for the symmetries of boundary geometry (flat plate channel vs. circular pipe) by a variational calculation for a large-scale energy length, which characterizes its bulk flow scaling by a simple exponent, i.e., m = 4 for the channel and 5 for the pipe. The predicted mean velocity shows excellent agreement with several dozen sets of quality empirical data for a wide range of the Reynolds number (Re), with a universal bulk flow constant k ≈ 0.45. Predictions for dissipation and turbulent transport in the bulk flow are also given, awaiting data verification.