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arXiv · 1606.00212

Bulk flow scaling for turbulent channel and pipe flows

Xi Chen·Fazle Hussain·Zhen-Su She
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Abstract

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. $m=4$ 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 $\kappa\approx0.45$. Predictions for dissipation and turbulent transport in the bulk flow are also given, awaiting data verification.

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Xi Chen, Fazle Hussain, Zhen-Su She. 2016-06-01. Bulk flow scaling for turbulent channel and pipe flows. https://doi.org/10.1209/0295-5075/115/34001

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