ANALYTICAL MODELING ON DISPERSION OF
NONCONSERVATIVE POLLUTANT ON
A STEP INCREASE IN DEPTH FLOW
Anton Purnama1, Easwaran Balakrishnan1,
Khaled S.M. Al-Mashrafi2
1Department of Mathematics, Sultan Qaboos University
Al-Khod PC 123, Muscat, OMAN
2Department of Basic Sciences, A'Sharqiyah University
PC 400, Ibra, OMAN

Abstract

Coastal wastewater-discharged effluents are likely to consist of pollutants with different dispersion and decay rates that vary with water depth. Mathematical models using a two dimensional advection-diffusion equation with a point source are presented to study the effects of a cross-stream sudden depth change and decay on mixing and dispersing steady discharge of non - conservative effluents. Analytical solutions are illustrated graphically by plotting contours of concentration, showing snapshots of discharged effluent plumes spreading. The shapes of effluent plumes across the cross-stream depth discontinuity line are significantly different, and thus the concentration at the discontinuity line is formulated to measure how much has effluents dispersed into or out of the shallow nearshore region.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 36
Issue: 4
Year: 2023

DOI: 10.12732/ijam.v36i4.8

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References

  1. [1] P.J.W. Roberts, H.J. Salas, F.M. Reef, M. Libhaber, A. Labe, J.C. Thom- son, Marine Wastewater Outfalls and Treatment Systems, International Water Association Publishing, London (2010).
  2. [2] Institution of Civil Engineers, Long Sea Outfalls, Thomas Telford Ltd., London (1989).
  3. [3] D.J. Gould, D. Munro, Relevance of microbial mortality to outfall design, Coastal Discharges - Engineering Aspect and Experience, Thomas Telford Ltd., London (1981), 45-50.
  4. [4] J.F. Macqueen, R.W. Preston, Cooling water discharges into a sea with a sloping bed, Water Research, 17, No 4 (1983), 389-395; https://doi.org/10.1016/0043-1354.
  5. [5] D.A. Roberts, E.L. Johnston, N.A. Knott, Impacts of desalination plants discharges on the marine environment: A critical review of published studies, Water Research, 44 (2010), 5117-5128; https://doi.org/10.1016/j.watres.2010.04.036.
  6. [6] A. Purnama, H.H. Al-Barwani, Spreading of brine waste discharges into the Gulf of Oman, Desalination, 195, No 1-3 (2006), 26-31; https://doi.org/10.1016/j.desal.2005.09.036.
  7. [7] N. Ahmad, R.E. Baddour, A review of sources, effects, disposal methods, and regulations of brine into marine environments, Ocean & Coastal Management, 87 (2014), 1-7; https://doi.org/10.1016/j.ocecoaman.2013.10.020.
  8. [8] S. Lattemann, T. Hopner, Environmental impact and impact assessment of seawater desalination, Desalination, 220, No 1-3 (2008), 1-15; https://doi.org/10.1016/j.desal.2007.03.009.
  9. [9] P. Mebine, R. Smith, Effects of contaminant decay on the diffusion centre of a river, Environmental Fluid Mechanics, 6 (2006), 101-114.
  10. [10] P. Mebine, R. Smith, Effect of pollutant decay on steady-state concentration distributions in variable depth flow, Environmental Fluid Mechanics, 9 (2009), 573-586.
  11. [11] A. Kay, The effect of cross-stream depth variations upon contaminant dispersion in a vertically well-mixed current, Estuarine and Coastal Shelf Science, 24 (1987), 177-204.
  12. [12] R. Smith, Effects of non-uniform currents and depth variations upon steady discharges in shallow water, Journal of Fluid Mechanics, 110 (1981), 373380.
  13. [13] A. Purnama, H.A. Al Maamari, E. Balakrishnan, Optimal outfall systems for nearshore effluent discharges on eroded sandy beaches, Journal of Coupled Systems and Multiscale Dynamics, 5, No 2-4 (2017), 217-224.
  14. [14] A. Purnama, H.A. Al-Maamari, E. Balakrishnan, Decay model for dispersion of coastal discharged effluents from multiport diffusers in the far-field, International Journal of New Innovations in Engineering and Technology, 12 (2019), 8-18.
  15. [15] A. Purnama, H.A. Al-Maamari, A.A. Al-Muqbali, E. Balakrishnan, The Effect of a step change in seabed depth on spreading discharged brine effluents from a two-outfall system, Journal of Mathematical and Computational Science, 10 (2020), 758-777; https://doi.org/10.28919/jmcs/4347.
  16. [16] D.A. Chin, P.J.W. Roberts, Model of dispersion in coastal waters, Journal of Hydraulic Engineering, 111 (1985), 12-28; https://doi/org/10.1061/(ASCE)0733-9429(1985)111:1(12).
  17. [17] I.R. Wood, Asymptotic solutions and behavior of outfall plumes, Journal of Hydraulic Engineering, 119 (1993), 553-580; https://doi.org/10.1061/(ASCE)0733-9429(1993)119:5(553).
  18. [18] C.H. Li, X.S. Pan, J. Ke, X.T. Dong, Comparison of 2D and 3D models of salinity numerical simulation, Polish Maritime Research, 22, No S1 (2015), 26-29; https://doi.org/10.1515/pomr-2015-0028.
  19. [19] D.L. Craig, H.J. Fallowfield, N.J. Cromar, Comparison of decay rates of faecal indicator organisms in recreational coastal water and sediment, Water Supply, 2 (2002), 131-138; https://doi.org/10.2166/ws.2002.0095.
  20. [20] A. Adcroft, R. Hallberg, J.P. Dunne, B.L. Samuels, J.A. Galt, Simulations of underwater plumes of dissolved oil in the Gulf of Mexico, Geophysical Research Letters, 37 (2010), L18605; https://doi.org/10.1029/2010GL044689.
  21. [21] V.P. Shukla, Analytical solutions for unsteady transport dispersion of nonconservative pollutant with time-dependent periodic waste discharge concentration, Journal of Hydraulic Engineering, 128 (2002), 866-869.
  22. [22] D.W. Ostendorf, Longshore dispersion over a flat beach, Journal of Geophysical Research, 87 (1982), 4241-4248.