A Mathematical Model for the Flow Resistance and the Related Hydrodynamic Dispersion Induced by River Dunes

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 induce...

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Bibliographic Details
Published in:Journal of Applied Mathematics 2013-01, Vol.2013 (2013), p.407-415-338
Main Authors: Pannone, Marilena, De Vincenzo, Annamaria, Brancati, Francesco
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Dunes
Flow resistance
Fluid flow
Geological research
Hydraulic measurements
Hydrodynamics
Hydrogeology
Mathematical analysis
Mathematical models
Mathematical research
Rivers
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Summary: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.
ISSN:1110-757X
1687-0042
DOI:10.1155/2013/432610