A Mathematical Model for the Flow Resistance and the Related Hydrodynamic Dispersion Induced by River DunesReport as inadecuate




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Journal of Applied MathematicsVolume 2013 2013, Article ID 432610, 9 pages

Research ArticleSchool of Engineering, University of Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy

Received 5 July 2013; Revised 1 October 2013; Accepted 1 October 2013

Academic Editor: Mohamed Fathy El-Amin

Copyright © 2013 Marilena Pannone et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Present work is aimed at the derivation of a simply usable equation for the total flow resistance associated with river bedforms, by a unifying approach allowing for bypassing some of the limiting restrictions usually adopted in similar types of studies. Specifically, we focused on the effect induced by the out-of-phase free surface undulations appearing in presence of sand dunes. The proposed expression, obtained by combining the balance of momentum referred to the control volume whose longitudinal dimension coincides with the dune wavelength and the energy balance integrated between its extreme sections, was tested by comparison with some laboratory experimental measurements available in the literature and referred to steady flow past fixed, variably rough bedforms. In terms of shear stress or friction factor, the proposed theory provides estimates in good agreement with the real data, especially if evaluated against the performances provided by other classical similar approaches. Moreover, when analyzed in terms of hydrodynamic dispersive properties as a function of the skin roughness on the basis of a previously derived analytical solution, the dune-covered beds seem to behave like meandering channels, responsible for a globally enhanced fluid particles longitudinal spreading, with a relatively reduced effect in the presence of less pronounced riverbed modelling.





Author: Marilena Pannone, Annamaria De Vincenzo, and Francesco Brancati

Source: https://www.hindawi.com/



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