Origin of the scaling laws of sediment transport

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences - Tập 473 Số 2197 - Trang 20160785 - 2017
Sk Zeeshan Ali1, Subhasish Dey2
1Sk Zeeshan Ali Google Scholar Find this author on PubMed
2Subhasish Dey http://orcid.org/0000-0002-1952-4491 [email protected] Google Scholar Find this author on PubMed

Tóm tắt

In this paper, we discover the origin of the scaling laws of sediment transport under turbulent flow over a sediment bed, for the first time, from the perspective of the phenomenological theory of turbulence. The results reveal that for the incipient motion of sediment particles, the densimetric Froude number obeys the ‘(1 +  σ )/4’ scaling law with the relative roughness (ratio of particle diameter to approach flow depth), where σ is the spectral exponent of turbulent energy spectrum. However, for the bedforms, the densimetric Froude number obeys a ‘(1 +  σ )/6’ scaling law with the relative roughness in the enstrophy inertial range and the energy inertial range. For the bedload flux, the bedload transport intensity obeys the ‘3/2’ and ‘(1 +  σ )/4’ scaling laws with the transport stage parameter and the relative roughness, respectively. For the suspended load flux, the non-dimensional suspended sediment concentration obeys the ‘ − Z ’ scaling law with the non-dimensional vertical distance within the wall shear layer, where Z is the Rouse number. For the scour in contracted streams, the non-dimensional scour depth obeys the ‘4/(3 −  σ )’, ‘−4/(3 −  σ )’ and ‘−(1 +  σ )/(3 −  σ )’ scaling laws with the densimetric Froude number, the channel contraction ratio (ratio of contracted channel width to approach channel width) and the relative roughness, respectively.

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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Tập 473 Số 2197

20160785

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