Theoretical Investigation into Longitudinal Dispersion in Natural Rivers — A Scaling Dispersion Model
(2002) Abstract
 Using a broad variety of scientific methods this dissertation systematically investigates the fundamental mechanisms underlying the dispersion processes in natural rivers and their mathematical descriptions in a geometrical framework. Emphasis is on the geometrical variations and irregularities of a natural river and their scales. Analysis starts with the integral scale and the Fickian dispersion in a straight channel by simply considering the influence of channel width to depth ratio on the dispersion and then a longitudinal dispersion coefficient equation containing the transverse mixing coefficient is derived. This equation is extended for meandering rivers by incorporating channel sinuosity. By taking account of the influence of... (More)
 Using a broad variety of scientific methods this dissertation systematically investigates the fundamental mechanisms underlying the dispersion processes in natural rivers and their mathematical descriptions in a geometrical framework. Emphasis is on the geometrical variations and irregularities of a natural river and their scales. Analysis starts with the integral scale and the Fickian dispersion in a straight channel by simply considering the influence of channel width to depth ratio on the dispersion and then a longitudinal dispersion coefficient equation containing the transverse mixing coefficient is derived. This equation is extended for meandering rivers by incorporating channel sinuosity. By taking account of the influence of smaller and smaller scale irregularities on the dispersion, a new dispersion mechanism, scaling dispersion, is presented to elucidate the physics underlying the nonFickian longitudinal dispersion processes of pollutants in natural rivers and thereby a scaling dispersion model is developed. The model is comprised of (1) a fractional advectiondispersionreaction equation (FRADRE), (2) methods for estimation of the parameters involved in the FRADRE, and (3) a numerical scheme devised to evaluate the solution of the FRADRE.
FRADRE is characterized by a fractional differential operator parameter F, called as fractor, reflecting the heterogeneity of natural media and acting on the dispersion term. The simplest form of the FRADRE is an integerorder diffusion equation and its solution is a semiinfinite Fourier probability distribution, leading to a new approach for estimation of the initial mixing length. FRADRE entails four parameters which can be estimated using a momentbased method developed by means of the Laplace Transform of fractional derivatives if field observations of dispersion processes are available. Results of parameter estimation show that the fractor F varies in the range of 1.4 – 2.0 with 1.65 possessing the maximum occurring frequency. In case of no detailed dye concentration test data, the longitudinal dispersion coefficient can be determined by the two methods derived from a channel shape equation for straight streams and from a more versatile channel shape equation for meandering rivers, respectively.
A numerical scheme, designated as F.3 Central FiniteDifference Scheme, is proposed for solution of the fractional partial differential equation FRADRE. The F.3 scheme recovers the conventional central finitedifference scheme when fractor F = 2. FRADRE can be numerically solved by applying the F.3 scheme for the fractional dispersion equation and the semiLagrangian method in conjunction with the natural cubicspline interpolation for the pure advection equation.
Dispersion characteristics computed by the scaling dispersion model were in excellent agreement with those observed by 20 dye tests conducted on the U.S. rivers, Mississippi, Missouri, Red, and Monocacy, thereby demonstrating the efficacy of the scaling dispersion model for prediction of the nonFickian dispersion processes in natural rivers. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/464811
 author
 Deng, ZhiQiang ^{LU}
 supervisor
 opponent

 Professor Cederwall, Klas, Royal Institute of Technology, Stockholm.
 organization
 publishing date
 2002
 type
 Thesis
 publication status
 published
 subject
 keywords
 soil mechanics, Väg och vattenbyggnadsteknik, Environmental technology, pollution control, Miljöteknik, kontroll av utsläpp, offshore technology, hydraulic engineering, Civil engineering, Scaling dispersion., Parameter estimation, Numerical scheme, Dispersion coefficient, Natural river
 pages
 192 pages
 publisher
 Department of Water Resources Engineering, Lund Institute of Technology, Lund University
 defense location
 Hall V:A, Department of Water Resources Engineering
 defense date
 20020830 10:15:00
 external identifiers

 other:ISRN:LUTVDG/TVVR1029(2002)
 language
 English
 LU publication?
 yes
 additional info
 Article: 1. Deng, Z.Q., Singh, V. P., and Bengtsson, L. (2001). “Longitudinal dispersion coefficient in straight rivers.” Journal of Hydraulic Engineering, ASCE, 127(11), 919927. Article: 2. Deng, Z.Q., and Singh, V. P. (1999). “Mechanism and conditions for change in channel pattern.” Journal of Hydraulic Research, IAHR, 37(4), 465478. Article: 3. Deng, Z.Q., Bengtsson, L., Singh, V. P., and Adrian, D. D. (2002). “Longitudinal dispersion coefficient in singlechannel streams.” Journal of Hydraulic Engineering, ASCE, 128(10), in press. Article: 4. Deng, Z.Q., Bengtsson, L., and Singh, V. P. (2002). “Scaling dispersion model for passive scalars in natural streams”, submitted to ASCE Journal of Hydraulic Engineering. Article: 5. Deng, Z.Q., Singh, V. P., and Bengtsson, L. (2002). “Numerical scheme for fractal advectiondispersion equation”, submitted to ASCE Journal of Hydraulic Engineering. Article: 6. Adrian, D. D., Singh, V. P., and Deng, Z.Q. (2002). “Diffusionbased semiinfinite Fourier probability distribution.” Journal of Hydrologic Engineering, ASCE, 7(2), 154167.
 id
 4af5da1ff0b0447db3e0ef37f97602a3 (old id 464811)
 date added to LUP
 20160401 16:31:34
 date last changed
 20181121 20:42:05
@phdthesis{4af5da1ff0b0447db3e0ef37f97602a3, abstract = {Using a broad variety of scientific methods this dissertation systematically investigates the fundamental mechanisms underlying the dispersion processes in natural rivers and their mathematical descriptions in a geometrical framework. Emphasis is on the geometrical variations and irregularities of a natural river and their scales. Analysis starts with the integral scale and the Fickian dispersion in a straight channel by simply considering the influence of channel width to depth ratio on the dispersion and then a longitudinal dispersion coefficient equation containing the transverse mixing coefficient is derived. This equation is extended for meandering rivers by incorporating channel sinuosity. By taking account of the influence of smaller and smaller scale irregularities on the dispersion, a new dispersion mechanism, scaling dispersion, is presented to elucidate the physics underlying the nonFickian longitudinal dispersion processes of pollutants in natural rivers and thereby a scaling dispersion model is developed. The model is comprised of (1) a fractional advectiondispersionreaction equation (FRADRE), (2) methods for estimation of the parameters involved in the FRADRE, and (3) a numerical scheme devised to evaluate the solution of the FRADRE.<br/><br> <br/><br> FRADRE is characterized by a fractional differential operator parameter F, called as fractor, reflecting the heterogeneity of natural media and acting on the dispersion term. The simplest form of the FRADRE is an integerorder diffusion equation and its solution is a semiinfinite Fourier probability distribution, leading to a new approach for estimation of the initial mixing length. FRADRE entails four parameters which can be estimated using a momentbased method developed by means of the Laplace Transform of fractional derivatives if field observations of dispersion processes are available. Results of parameter estimation show that the fractor F varies in the range of 1.4 – 2.0 with 1.65 possessing the maximum occurring frequency. In case of no detailed dye concentration test data, the longitudinal dispersion coefficient can be determined by the two methods derived from a channel shape equation for straight streams and from a more versatile channel shape equation for meandering rivers, respectively.<br/><br> <br/><br> A numerical scheme, designated as F.3 Central FiniteDifference Scheme, is proposed for solution of the fractional partial differential equation FRADRE. The F.3 scheme recovers the conventional central finitedifference scheme when fractor F = 2. FRADRE can be numerically solved by applying the F.3 scheme for the fractional dispersion equation and the semiLagrangian method in conjunction with the natural cubicspline interpolation for the pure advection equation.<br/><br> <br/><br> Dispersion characteristics computed by the scaling dispersion model were in excellent agreement with those observed by 20 dye tests conducted on the U.S. rivers, Mississippi, Missouri, Red, and Monocacy, thereby demonstrating the efficacy of the scaling dispersion model for prediction of the nonFickian dispersion processes in natural rivers.}, author = {Deng, ZhiQiang}, language = {eng}, publisher = {Department of Water Resources Engineering, Lund Institute of Technology, Lund University}, school = {Lund University}, title = {Theoretical Investigation into Longitudinal Dispersion in Natural Rivers — A Scaling Dispersion Model}, year = {2002}, }