Phys. Rev. Lett. 88, 014501 (2001) [4 pages]Scaling and Similarity in Rough Channel FlowsReceived 21 June 2001; published 17 December 2001 We show that Manning's empirical formula for the mean velocity of turbulent flows in channels represents the power-law asymptotic behavior of a flow of incomplete similarity in the relative roughness. We then derive the formula based on the phenomenological theory of turbulence. Our derivation yields the correct similarity exponent; it justifies Manning's use of a single parameter, the hydraulic radius, to characterize the geometry of the cross section; and it affords insight into the mechanism of momentum transfer. © 2002 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.88.014501
DOI:
10.1103/PhysRevLett.88.014501
PACS:
47.27.Nz
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