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Environmental Science and Pollution Research

, Volume 26, Issue 30, pp 30675–30683 | Cite as

Theoretical analysis of pollutant mixing zone considering lateral distribution of flow velocity and diffusion coefficient

  • Zhouhu WuEmail author
  • Wen Wu
Water Environment Protection and Contamination Treatment
  • 66 Downloads

Abstract

Theoretical formulae have shown significant advantages in describing the characteristic geometric scales of the pollutant mixing zone (PMZ) formed by offshore pollutant discharged by a single general form. They, however, fail to predict the influence of the lateral inhomogeneity of the river flow because constant flow velocity and the lateral diffusion coefficient are assumed during the derivation. The realistic flow velocity in a river is fitted by an exponential law in this study and the lateral diffusion coefficient is proposed to have the same form. Similar idea has been used in previous studies on the vertical dispersion of scalar in the lower atmosphere. Pollutant discharged from a steady onshore point source into a wide straight open channel is examined to characterize the concentration taking into consideration of these lateral variations. Theoretical formulae describing the maximum length, maximum width and its corresponding longitudinal position, as well as the area of the PMZ are derived. A non-dimensional standard curve equation for the isoconcentration boundary of PMZ is also obtained. The results show that the shape of the dimensionless standard curve of PMZ depends only on the exponential constants in the exponential laws. The exponential profiles that fit the near-shore velocity give good prediction, while the ones that match the entire lateral range up to the center of the river underpredict the PMZ significantly. These findings are of great importance for practitioners to characterize the geometry of the PMZ in rivers and for water quality modeling.

Keywords

River velocity distribution Lateral diffusion coefficient Exponential distribution law Pollutant concentration distribution Pollutant mixing zone Geometric characteristic scale 

Notes

Funding information

This research is supported by the National Natural Science Foundation of China (51379097, 50979036).

References

  1. Baek KO, Seo IW (2010) Routing procedures for observed dispersion coefficients in two-dimensional river mixing. Adv Water Resour 33:1551–1559CrossRefGoogle Scholar
  2. Baek KO, Seo IW (2016) On the methods for determining the transverse dispersion coefficient in river mixing. Adv Water Resour 90:1–9CrossRefGoogle Scholar
  3. Baek KO, Seo IW (2017) Estimation of the transverse dispersion coefficient for two-dimensional models of mixing in natural streams. J Hydro Environ Res 15:67–74CrossRefGoogle Scholar
  4. Baek KO, Seo IW, Jeong SJ (2006) Evaluation of dispersion coefficients in meandering channels from transient tracer tests. J Hydraul Eng 132(10):1021–1032CrossRefGoogle Scholar
  5. Beltaos S (1980) Transverse mixing tests in natural streams. J Hydraul Div 106(10):1607–1625Google Scholar
  6. Deng ZQ, Jung HS (2009) Scaling dispersion model for pollutant transport in river. Environ Model Softw 24:627–631CrossRefGoogle Scholar
  7. Elder JW (1959) The dispersion of marked fluid in turbulent shear flow. J Fluid Mech 5(12):544–560CrossRefGoogle Scholar
  8. Fischer HB, Hanamura T (1975) The effect of roughness strips on transverse mixing in hydraulic models. Water Resour Res 11(2):362–364CrossRefGoogle Scholar
  9. Fischer HB, Imberger J, List EJ et al (1979) Mixing in inland and coastal waters. Academic, New York, pp 104–112CrossRefGoogle Scholar
  10. Holley ER, Abraham G (1973) Field tests of transverse mixing in rivers. J Hydraul Div 99(12):2313–2331Google Scholar
  11. Huang ZL, Li YL, Chen YC (2006) Water quality prediction and water environmental carrying capacity calculation for Three Gorges Reservoir. China Water Resources and Hydropower Press, Beijing, pp 168–177Google Scholar
  12. IDEQ (2015) Mixing zone technical procedures manual (draft). Idaho Department of Environmental Quality, BoiseGoogle Scholar
  13. Lau YL, Krishnappan BG (1977) Transverse dispersion in rectangular channels. J Hydraul Div 103(10):1173–1189Google Scholar
  14. Li WH (1972) Differential equations of hydraulic transients, dispersion and ground water flow. Prentice Hall, Englewood Cliffs, pp 180–184Google Scholar
  15. Lu JY, Zhan YZ, Zhao GS et al (2012) Study on cross sectional velocity distribution affected by sidewall in river channel. J Hydraul Eng 43(6):645–652 658. (in Chinese)Google Scholar
  16. Lung WS (1995) Mixing-zone modeling for toxic waste-load allocations. J Environ Eng 121(11):839–842CrossRefGoogle Scholar
  17. Miller AC, Richardson EV (1974) Diffusion and dispersion in open channel flow. J Hydraul Div 100(1):68–74Google Scholar
  18. Okoye JK (1970) Characteristics of transverse mixing in open-channel flows. California Institute of TechnologyGoogle Scholar
  19. Pasquill F (1974) Atmospheric diffusion, 2nd edn. Wiley, New York, p 429Google Scholar
  20. Rodríguez Benítez AJ, Gómez AG, Díaz CÁ (2016) Definition of mixing zones in rivers. Environ Fluid Mech 16(1):209–244CrossRefGoogle Scholar
  21. Wang P, Chen GQ (2016) Solute dispersion in open channel flow with bed absorption. J Hydrol 543(Part B):208–217CrossRefGoogle Scholar
  22. Wang P, Chen GQ (2017a) Concentration distribution for pollutant dispersion in a reversal laminar flow. J Hydrol 551:151–161CrossRefGoogle Scholar
  23. Wang P, Chen GQ (2017b) Contaminant transport in wetland flows with bulk degradation and bed absorption. J Hydrol 552:674–683CrossRefGoogle Scholar
  24. Webel G, Schatzmann M (1984) Transverse mixing in open channel flow. J Hydraul Eng 110(4):423–435CrossRefGoogle Scholar
  25. Wu ZH (2015) Analytical calculation of the depth-averaged concentration distribution and pollutant mixing zone for sloped-bank. J Hydraul Eng 46(10):1172–1180 (in Chinese)Google Scholar
  26. Wu ZH, Jia HY (2009) Analytic method for pollutant mixing zone in river. Adv Water Sci 20(4):544–548 (in Chinese)Google Scholar
  27. Wu ZH, Wu W, Wu GZ (2011) Calculation method of lateral and vertical diffusion coefficients in wide straight rivers and reservoirs. J Comp 6(6):1102–1109Google Scholar
  28. Wu W, Wu ZH, Song ZW (2017) Calculation method for steady-state pollutant concentration in mixing zones considering variable lateral diffusion coefficient. Water Sci Technol 76(1):201–209CrossRefGoogle Scholar
  29. Zhang YL, Li YL (1993) A guide to analytical solution of pollutant mixing zone. Ocean Press, BeijingGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Environmental and Municipal EngineeringQingdao University of TechnologyQingdaoChina
  2. 2.Department of Mechanical EngineeringJohns Hopkins UniversityBaltimoreUSA

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