Longitudinal Dispersion in River Flows Characterized by Random Large-Scale Bed Irregularities: First-Order Analytical Solution
Publication: Journal of Hydraulic Engineering
Volume 138, Issue 5
Abstract
A stochastic Lagrangian approach is proposed for the analytical derivation of a longitudinal dispersion coefficient that accounts for both transverse and longitudinal flow field variability in straight-axis open channels characterized by longitudinal large-scale bed heterogeneity, that is, by longitudinal bed irregularities over a wide range of representative lengths, from the simple grain roughness to large undulations (up to order of kilometers), possibly related to topographical discontinuities or to extended and inhomogeneous depositional processes carried out by natural or anthropogenic agents. The resulting dimensionless expression, involving the average Chezy coefficient and the ratios of river width and longitudinal heterogeneity correlation length to the average flow depth, is obtained at the first order in the depth fluctuations as a time-dependent function given by the sum of three distinct components. The first main component is related to the transverse velocity distribution and would apply even for truly uniform flows; the second component comes from the moderate longitudinal nonuniformity and under certain conditions can reach values of comparable order of magnitude; finally, the third component, originating from the cross contribution of transverse and longitudinal velocity variability, is always quantitatively insignificant. While the numerical validation of the linearized formulation was already illustrated and discussed in a previous paper with reference to ideally two-dimensional streams, the present work includes, among other things, a comparison of the performances provided by the asymptotic version of the transversally generated dispersion component and three earlier empirical or semianalytical formulas, based on field measurements documented in the literature.
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Information
Published In
Journal of Hydraulic Engineering
Volume 138 • Issue 5 • May 2012
Pages: 400 - 411
Copyright
© 2012. American Society of Civil Engineers.
History
Received: Aug 26, 2010
Accepted: Nov 17, 2011
Published online: Apr 16, 2012
Published in print: May 1, 2012
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