Skip to main content
Log in

Longitudinal Dispersion Subjected to Rigid Vegetation in a Channel

  • Water Resources and Hydrologic Engineering
  • Published:
KSCE Journal of Civil Engineering Aims and scope

Abstract

Estimation of longitudinal dispersion coefficient is an important parameter for dispersion of the contaminants and hence can be used in any river water quality management intervention. Since the natural river water body is dominated by the presence of vegetation, it is expected that the longitudinal dispersion coefficient will be affected by the presence or absence of the vegetation. Hence in this study the effect of vegetation on longitudinal dispersion coefficient has been studied. Experiments have been conducted in a channel having rigid vegetation using rhodamine as tracer and concentrations of rhodamine is measured at various time intervals at 2 and 4 m downstream from the point of injection. The longitudinal dispersion coefficient is determined in the presence as well as absence of vegetation in the channel having Reynolds number varying from 2500–10000 and Froude’s number varying from 0.02-0.05. It is found that the longitudinal dispersion coefficient downstream to the vegetation is affected in the presence of the vegetation. It is also found that the dispersion coefficient depends on number of rows of vegetation but significantly depends on the diameter of vegetation. A new functional relationship between dimensionless terms is derived using dimensional analysis for predicting the dispersion coefficient.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ahmad, Z. (2003). “Estimation of longitudinal dispersion coefficient.” ISH Journal of Hydraulic Engineering, vol. 9, no. 1, pp. 14–28. DOI: 10.1080/09715010.2003.10514722.

    Article  Google Scholar 

  • Ahmad, Z. (2007). “Effect of channel cross-section on mixing length.” ISH Journal of Hydraulic Engineering, vol. 13, no. 1, pp. 1–17. DOI: 10.1080/09715010.2007.10514854.

    Article  Google Scholar 

  • Ahmad, Z. (2009). “Mixing length for establishment of longitudinal dispersion in streams.” International Journal of Modeling and Simulation, vol. 29, no. 2, pp. 127–136. DOI: 10.1080/02286203. 2009.11442518.

    Article  Google Scholar 

  • Ahmad, Z., Kothyari, U. C., and Ranga Raju, K. G. (1999). “Longitudinal dispersion in open channel.” ISH Journal of Hydraulic Engineering, vol. 5, no. 2, pp. 1–21. DOI: 10.1080/09715010.1999.10514649.

    Article  Google Scholar 

  • Azamathulla, H. M. and Ghani, A. (2011). “Genetic programming for predicting longitudinal dispersion coefficients in streams.” Water Resources Management, vol. 25, no. 6, pp. 1537–1544. DOI: 10.1007/s11269-010-9759-9.

    Article  Google Scholar 

  • Babbar, R. and Joshi, H. (2008). “Empirical validation of field estimated dispersion coefficient for a tropical river.” Asian Journal of Water, Environment and Pollution, vol. 5, no. 3, pp. 73–78.

    Google Scholar 

  • Brady, J. A. and Johnson, P. (1981). “Predicting times of travel, dispersion and peak concentrations of pollution incidents in streams.” Journal of Hydrology, vol. 53, Nos. 1–2, pp. 135–150. DOI: 10.1016/0022-1694(81)90041-X.

    Article  Google Scholar 

  • Day, T. J. (1975). “Longitudinal dispersion in natural channels.” Water Resources Research, vol. 11, no. 6, pp. 909–918. DOI: 10.1029/WR011i006p00909.

    Article  Google Scholar 

  • Fischer, H. B. (1967). “The mechanics of dispersion in natural streams.” Journal of Hydraulics Division, ASCE, vol. 93, no. 6, pp. 187–216.

    Google Scholar 

  • Fischer, H. B. (1968). “Dispersion predictions in natural streams.” Journal of Sanit. Eng. Div., ASCE, vol. 94, no. 5, pp. 927–943.

    Google Scholar 

  • Fischer, H. B. (1973). “Longitudinal dispersion and turbulent mixing in open channel flow.” Rev. Fluid Mechanics, vol. 5, pp. 59–77.

    Article  MATH  Google Scholar 

  • Giraldi, D., Vitturi, M. M., Zaramella, M., Marion, A., and Iannelli, R. (2009). “Hydrodynamics of vertical subsurface flow constructed wetlands: Tracer test with rhodamine WT and numerical modeling.” Ecological Engineering, vol. 35, pp. 265–273. DOI: 10.1016/j.ecoleng.2008.06.004.

    Article  Google Scholar 

  • Guymer, I. (1998). “Longitudinal dispersion in sinuous channel with changes in shape.” Journal of Hydraulic Engineering, ASCE, vol. 124, no. 1, pp. 33–40.

    Article  Google Scholar 

  • Hamidifar, H., Omid, M. H., and Keshavarzi, A. (2015). “Longitudinal dispersion in waterways with vegetated floodplain.” Ecological Engineering, vol. 84, pp. 398–407. DOI: 10.1016/j.ecoleng.2015.0.048.

    Article  Google Scholar 

  • Ho, D. T., Schlosser, P., and Caplow, T. (2002). “Determination of longitudinal dispersion coefficient and net advection in the tidal Hudson river with a large scale, high resolution SF6 tracer release experiment.” Environmental Science Technology, vol. 36, no. 15, pp. 3234–3241. DOI: 10.1021/es015814+.

    Article  Google Scholar 

  • Kim, D. (2012). “Assessment of longitudinal dispersion coefficients using acoustic Doppler current profilers in large river.” Journal of Hydro-Environment Research, vol. 6, no. 1, pp. 29–39. DOI: 10.1016/j.jher.2011.06.001.

    Article  Google Scholar 

  • Lightbody, A. F. and Nepf, H. M. (2006). “Prediction of velocity profiles and longitudinal dispersion in emergent salt marsh vegetation.” Limnol. Oceangraphy, vol. 51, no. 1, pp. 218–228. DOI: 10.4319/lo.2006.51.1.0218.

    Article  Google Scholar 

  • Murphy, E., Ghisalberti, M., and Nepf, H. (2007). “Models and laboratory study of dispersion in flows with submerged vegetation.” Water Resources Research, vol. 43, no. 5, pp. 1–12. DOI: 10.1029/2006WR005229.

    Article  Google Scholar 

  • Nepf, H. M. (1999). “Drag Turbulence and diffusion in flow through emergent vegetation.” Water Resources Research, vol. 35, no. 2, pp. 479–489. DOI: 10.1029/1998WR900069.

    Article  Google Scholar 

  • Nepf, H. M. and Ghisalberti, M. (2008). “Flow and transport in channels with submerged vegetation.” Acta Geophys, vol. 56, no. 3, pp. 753–777. DOI: 10.2478/s11600-008-0017-y.

    Article  Google Scholar 

  • Nepf, H. M., Ghisalberti, M., White, B., and Murphy, E. (2007). “Retention time and dispersion associated with submerged aquatic canopies.” Water Resources Research, vol. 43, no. 4, pp. 1–10. DOI: 10.1029/2006WR005362.

    Article  Google Scholar 

  • Nepf, H. M., Mugnier, C. G., and Zavistoski, R. A. (1997a). “The effect of vegetation on longitudinal dispersion.” Estuarine, Coastal and Shelf Science, vol. 44, no. 6, pp. 675–684. DOI: 10.1006/ecss.1996. 0169.

    Article  Google Scholar 

  • Nepf, H. M., Sullivan, J. A., and Zavistoski, R. A. (1997b). “A model for diffusion within emergent vegetation.” Limnol. Oceangraphy, vol. 42, no. 8, pp. 1735–1745.

    Article  Google Scholar 

  • Nepf, H. M. and Vivoni, E. R. (2000). “Flow structure in depth-limited, vegetated flow.” Journal of Geophysical Research, Vol. 105, No. C12, pp. 28547–28557. DOI: 10.1029/2000JC900145.

    Google Scholar 

  • Perucca, E., Camporeale, C., and Ridolfi, L. (2009). “Estimation of the dispersion coefficient in rivers with riparian vegetation.” Adv. Water Resources, vol. 32, no. 1, pp. 78–87. DOI: 10.1016/j.advwatres. 2008.10.007.

    Article  Google Scholar 

  • Seo, W. and Cheong, T. S. (1998). “Predicting longitudinal dispersion coefficient in natural streams.” Journal of Hydraulic Engineering, ASCE, vol. 124, no. 1, pp. 25–32.

    Article  Google Scholar 

  • Serra, T., Fernando, H. J. S., and Rodriguez, R. V. (2004). “Effects of emergent vegetation on lateral diffusion in wetlands.” J. Water. Res., vol. 38, no. 1, pp. 139–147. DOI: 10.1016/j.watres.2003.09.009.

    Article  Google Scholar 

  • Shucksmith, J. D., Boxall, J. B., and Guymer, I. (2011). “Determining longitudinal dispersion coefficients for submerged vegetated flow.” Water Resources Research, vol. 47, no. 10, pp. 1–13. DOI: 10.1029/2011WR010547.

    Article  Google Scholar 

  • Singh, S. K. and Beck, M. B. (2003). “Dispersion coefficient of streams from tracer experiment data.” Journal of Environmental Engineering, ASCE, vol. 129, no. 6, pp. 539–546.

    Article  Google Scholar 

  • Taylor, G. I. (1953). “Dispersion of soluble matter in solvent flowing slowly through a tube.” Proc. Royal Soc. London Ser A, vol. 219, no. 1137, pp. 186–203.

    Article  Google Scholar 

  • Taylor, G. I. (1954). “The dispersion of matter in turbulent flow through a pipe.” Proc. Royal Soc. London Ser A, Royal Society Publishing, vol. 223, no. 1155, pp. 446–468.

    Article  Google Scholar 

  • Tealdi, S., Camporeale, C., Perucca, E., and Ridolfi, L. (2010). “Longitudinal dispersion in vegetated rivers with stochastic flows.” Adv. Water Resources, vol. 33, no. 5, pp. 562–571. DOI: 10.1016/j.advwatres. 2010.03.003.

    Article  Google Scholar 

  • Toprak, Z. F., Hamidi, N., Kisi, O., and Gerger, R. (2014). “Modeling dimensionless longitudinal dispersion coefficient in natural streams using Artificial Intelligence methods.” KSCE Journal of Civil Engineering, vol. 18, no. 2, pp. 718–730. DOI: 10.1007/s12205-014-0089-y.

    Article  Google Scholar 

  • White, B. L. and Nepf, H. M. (2003). “Scalar transport in random cylinder arrays at moderate Reynolds number.” J. Fluid. Mechanics, vol. 487, pp. 43–79. DOI: 10.1017/S0022112003004579.

    Article  MATH  Google Scholar 

  • Zeng, L., Chen, G. Q., Tang, H. S., and Wu, Z. (2011). “Environmental dispersion in wetland flow.” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 1, pp. 206–215. DOI: 10.1016/j.cnsns.2010.02.019.

    Article  MathSciNet  MATH  Google Scholar 

  • Zeng, Y. H. and Huai, W. X. (2014). “Estimation of longitudinal dispersion coefficient in rivers.” Journal of Hydro-Environment Research, vol. 8, no. 1, pp. 2–8. DOI: 10.1016/j.jher.2013.02.005.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Dwarikanath Ratha.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ratha, D., Chandra, A., Babbar, R. et al. Longitudinal Dispersion Subjected to Rigid Vegetation in a Channel. KSCE J Civ Eng 22, 5242–5252 (2018). https://doi.org/10.1007/s12205-017-2894-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12205-017-2894-6

Keywords

Navigation