Longitudinal Dispersion in Natural Streams

Beer, Tom; Young, Peter C.

doi:10.1061/(asce)0733-9372(1983)109:5(1049)

Cited by 149 publications

(79 citation statements)

References 30 publications

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“…The Aggregated Dead Zone (ADZ) model has been used for modelling solute dispersion in rivers for many years [Beer andYoung, 1983, Young andWallis, 1993]. The Semi-Distributed ADZ (SDADZ) model is constructed rather simply by a chain of suitably small ADZ elements connected in series, parallel or even feedback (should this relate to a physically meaningful situation).…”

Section: The Quasi-distributed Adz Modelmentioning

confidence: 99%

Continuous-Time Emulation of Large Distributed Parameter Dispersion Models.

Young

2012

IFAC Proceedings Volumes

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Section: The Quasi-distributed Adz Modelmentioning

confidence: 99%

Continuous-Time Emulation of Large Distributed Parameter Dispersion Models.

Young

2012

IFAC Proceedings Volumes

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“…Physical-mathematical models can be applied to model the dispersion process. When the vertical and transverse homogeneity are complete, the most commonly used models are Taylor's [1954] model, Chatwin's [1980] model, cells or compartments in series (CIS) [Levenspiel, 1979], and combined models of plug flow and compartments in series, such as the aggregated dead zone (ADZ) model [Beer and Young, 1983;Wallis et al, 1989;Young, 1999 andNatale, 2000]. The use of these models requires the knowledge of the dispersion characteristics or model parameters for the river studied.…”

Section: Introductionmentioning

confidence: 99%

“…The use of these models requires the knowledge of the dispersion characteristics or model parameters for the river studied. These parameters are (1) the longitudinal dispersion coefficient, D L , which is used in the Taylor [1954] method; (2) the distribution moments, which are used with the Chatwin [1980] method; (3) the number of completely mixed compartments, the residence time of each compartment, which are used in the CIS model [Levenspiel, 1979] and (4) the number of completely mixed compartments, the residence time of each compartment and the associate advective time delay, if the ADZ model is used [Beer and Young, 1983;Wallis et al, 1989;Natale, 2000]. All of the above parameters contain similar information about the dispersion capacity of the stream and they have been interrelated by several authors [Levenspiel, 1979;Smith, 1957;Aris, 1959;Chatwin, 1980].…”

Section: Introductionmentioning

confidence: 99%

Determining the dispersion characteristics of rivers from the frequency response of the system

Lambertz

Palancar

Aragón

et al. 2006

Water Resources Research

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[1] A new method of determining the parameters of an aggregated dead zone model (ADZ) to predict longitudinal dispersion in rivers is presented. The method is based on the frequency response analysis (FRA) of observed field tests, which consist of tracer injections (input) and measurement of tracer in downstream sampling points (output) located downstream from the injection point. The ADZ is a combination of plug and completely mixed flow compartments. The ADZ parameters (number of compartments, mean residence time, and delay time) are evaluated by means of Bode plots that give the system order (number of compartments), gain, time constant (mean residence time of each compartment) and delay time. The FRA-ADZ method was checked with tracer data runs in two Spanish rivers, the Tagus and the Ebro rivers. The experimental tracer concentration versus time distributions were compared with the ADZ predicted curves, which were calculated using parameters obtained from the FRA method, and with curves predicted by several classical models. The residence time of several reaches within the two studied rivers was predicted by the FRA-ADZ method with a relative error lower than 10%. The method is generally applicable to ideal and nonideal inputs and is particularly well suited to arbitrary-shaped initial source concentration distributions.Citation: Lambertz, P., M. C. Palancar, J. M. Aragón, and R. Gil (2006), Determining the dispersion characteristics of rivers from the frequency response of the system, Water Resour. Res., 42, W09414,

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“…3 Since, for a constant pressure gradient the fluid flux varies with curvature and torsion-generally first decreasing with increasing torsion then later increasing with torsion (see Yamamoto, Yanase, and Yoshida [40] and its correction [41])-it follows that the mean pressure gradient (26) varies along a generally curving pipe. To check my 2 As discussed by Berger, Talbot, and Yao [3, section 2.1.1.2], there are various and conflicting definitions of the Dean number: Berger, Talbot, and Yao recommended the use of Dn = 2 √ κ Re, which I have adopted here. This Dean number could be viewed as √ κ Re for a Reynolds number based upon the pipe diameter rather than the radius that I have used.…”

Section: Introductionmentioning

confidence: 99%

Shear Dispersion along Circular Pipes Is Affected by Bends, but the Torsion of the Pipe Is Negligible

Roberts

2004

SIAM J. Appl. Dyn. Syst.

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Abstract. The flow of a viscous fluid along a curving pipe of fixed radius is driven by a pressure gradient. For a generally curving pipe it is the fluid flux which is constant along the pipe, and so I extend fluid flow solutions of Dean [W. R. Dean, Phil. Mag., 5 (1928) , 219 (1953), pp. 186-203] and its refinements. However, two conflicting effects occur in a generally curving pipe: viscosity skews the velocity profile which enhances the shear dispersion, whereas in faster flow centrifugal effects establish secondary flows that reduce the shear dispersion. The two opposing effects cancel at a Reynolds number of about 15. Interestingly, the torsion of the pipe seems to have very little effect upon the flow or the dispersion; the curvature is by far the dominant influence. Last, curvature and torsion in the fluid flow significantly enhance the upstream tails of concentration profiles in qualitative agreement with observations of dispersion in river flow.

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Longitudinal Dispersion in Natural Streams

Cited by 149 publications

References 30 publications

Continuous-Time Emulation of Large Distributed Parameter Dispersion Models.

Continuous-Time Emulation of Large Distributed Parameter Dispersion Models.

Determining the dispersion characteristics of rivers from the frequency response of the system

Shear Dispersion along Circular Pipes Is Affected by Bends, but the Torsion of the Pipe Is Negligible

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