Phenomenological description of scaling laws of sediment transport

Subhasish Dey,Sk Zeeshan Ali,A Paquier,N Rivière

doi:10.1051/e3sconf/20184004001

Subhasish Dey, Sk Zeeshan Ali + Show 2 more

Open Access

https://doi.org/10.1051/e3sconf/20184004001

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Abstract

In this paper, we seek the scaling laws of sediment transport under a turbulent flow by applying the phenomenological theory of turbulence. The results show that at the threshold of sediment motion, the densimetric Froude number follows a “(1+σ)/4” scaling law with the relative roughness number (ratio of particle size to flow depth), where σ is the spectral exponent. For the bedload transport, the bedload transport intensity follows a “3/2” and “(1+σ)/4” scaling laws with the transport stage function and the relative roughness, respectively. For the scour in a contracted stream, the dimensionless scour depth follows a “4/(3–σ)”, “– 4/(3–σ)” and “–(1+σ)/(3–σ)” scaling laws with the densimetric Froude number, the channel contraction ratio and the relative roughness, respectively.

Highlights

The phenomenological theory of turbulence was accredited to Kolmogorov’s [1] pioneering contributions to the scaling laws of the fully developed homogeneous and isotropic turbulence
We apply the laws of turbulent energy spectrum together with the momentum transfer theory to find the link between the laws of sediment transport and the turbulent energy spectrum
The scaling laws of sediment transport under turbulent flow are sought from the perspective of the phenomenological theory of turbulence

Summary

Introduction

The phenomenological theory of turbulence was accredited to Kolmogorov’s [1] pioneering contributions to the scaling laws of the fully developed homogeneous and isotropic turbulence. The phenomenological theory allows us to anticipate the scaling laws of classical problems of sediment transport in a simplified way demanding less heuristic arguments. The advantage of this theory to analyse a problem is that this theory provides a universal relationship, unlike the empirical laws, by linking the dependent and the independent variables. This theory cannot predict the multiplicative constant linking the dependent and the independent variables and the multiplicative constant must be obtained from experimental data. The phenomenological theory of turbulence was applied to obtain the similarity laws in open-channel flows [3].

Spectral laws of turbulence

Scaling law of threshold velocity

Scaling law of bedload transport rate

Conclusion