A Centre Manifold Description of Contaminant Dispersion in Channels with Varying Flow Properties

Mercer, G. N.; Roberts, A. J.

doi:10.1137/0150091

Cited by 160 publications

(216 citation statements)

References 24 publications

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“…Unfortunately, our procedure then leads to higher order differential operators and it is not clear if they are easy to handle. In the absence of the boundaries, higher order terms were determined in [13] using the program REDUCE.…”

Section: The Transversal Peclet Number and Damentioning

confidence: 99%

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Rigorous Upscaling of the Reactive Flow through a Pore, under Dominant Peclet and Damkohler Numbers

Mikelić¹,

Devigne²,

Duijn³

2006

SIAM J. Math. Anal.

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Section: The Transversal Peclet Number and Damentioning

confidence: 99%

“…The most convincing is the near rigorous derivation using the center manifold theory by Mercer and Roberts [13]. In this paper the initial value problem is studied and the Fourier transform with respect to x is applied.…”

Section: Introductionmentioning

confidence: 99%

Rigorous Upscaling of the Reactive Flow through a Pore, under Dominant Peclet and Damkohler Numbers

Mikelić¹,

Devigne²,

Duijn³

2006

SIAM J. Math. Anal.

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“…Let us show how this problem is formulated mathematically. Performing the Fourier transformation of (2.1), one gets [3] We reformulate our dispersion problem to make it similar to Eq. (A.1).…”

Section: Appendix A2 Dispersion In Shear Flows With Longitudinal DImentioning

confidence: 99%

“…The variation of u along this line is sought in the IRBF form. The second-order derivative of u is decomposed into RBFs; the RBF network is then integrated once and twice to obtain the expressions for the first-order derivative of u and the solution u itself, 3) where…”

Section: Second-order 1d-irbfn (1d-irbfn-2 Scheme)mentioning

confidence: 99%

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Modelling dispersion in laminar and turbulent flows in an open channel based on centre manifolds using 1D-IRBFN method

Mohammed

Ngo-Cong

Strunin

et al. 2014

Applied Mathematical Modelling

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Centre manifold method is an accurate approach for analytically constructing an advection-diffusion equation (and even more accurate equations involving higher-order derivatives) for the depth-averaged concentration of substances in channels. This paper presents a direct numerical verification of converge to each other, with their velocities becoming practically equal. The obtained numerical results also demonstrate that the longitudinal diffusion can be neglected compared to the advection.

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Predictability of tracer dilution in large open channel flows: Analytical solution for the coefficient of variation of the depth‐averaged concentration

Pannone

2014

Water Resources Research

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A large-time analytical solution is proposed for the spatial variance and coefficient of variation of the depth-averaged concentration due to instantaneous, cross sectionally uniform solute sources in pseudorectangular open channel flows. The mathematical approach is based on the use of the Green functions and on the Fourier decomposition of the depth-averaged velocities, coupled with the method of the images. The variance spatial trend is characterized by a minimum at the center of the mass and two mobile, decaying symmetrical peaks which, at very large times, are located at the inflexion points of the average Gaussian distribution. The coefficient of variation, which provides an estimate of the expected percentage deviation of the depth-averaged point concentrations about the section-average, exhibits a minimum at the center which decays like t 21 and only depends on the river diffusive time scale. The defect of crosssectional mixing quickly increases with the distance from the center, and almost linearly at large times. Accurate numerical Lagrangian simulations were performed to validate the analytical results in preasymptotic and asymptotic conditions, referring to a particularly representative sample case for which crosssectional depth and velocity measurements were known from a field survey. In addition, in order to discuss the practical usefulness of computing large-time concentration spatial moments in river flows, and resorting to directly measured input data, the order of magnitude of section-averaged concentrations and corresponding coefficients of variation was estimated in field conditions and for hypothetical contamination scenarios, considering a unit normalized mass impulsively injected across the transverse section of 81 U.S. rivers.

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A Centre Manifold Description of Contaminant Dispersion in Channels with Varying Flow Properties

Cited by 160 publications

References 24 publications

Rigorous Upscaling of the Reactive Flow through a Pore, under Dominant Peclet and Damkohler Numbers

Rigorous Upscaling of the Reactive Flow through a Pore, under Dominant Peclet and Damkohler Numbers

Modelling dispersion in laminar and turbulent flows in an open channel based on centre manifolds using 1D-IRBFN method

Predictability of tracer dilution in large open channel flows: Analytical solution for the coefficient of variation of the depth‐averaged concentration

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