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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 versus circular pipe) by a variational calculation for a large-scale
energy length, which characterizes its bulk flow scaling by a simple exponent,
i.e. for channel and 5 for 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
. Predictions for dissipation and turbulent transport in the
bulk flow are also given, awaiting data verification.Comment: 4 pages, 4 figure
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