, Volume 27, Issue 4, pp 571–582 | Cite as

On the mixing processes in estuaries: The fractional freshwater method revisited

  • P. Regnier
  • J. P. O'Kane


A mathematically transparent model for long-term solute dynamics, based on an oscillating reference frame, is applied to the analysis of the mixing process in estuaries. Classical tidally-averaged transport models for estuaries, all derived in some way from the Fractional Freshwater Method of Ketchum (1951) are reinterpreted in this framework. We demonstrate that in these models, the dispersion coefficients obtained from salinity profiles are not always a good representation of the mixing intensity of other dissolved constituents. In contrast, the hypothesis of equal coefficients is always verified in our oscillating coordinate system, which is almost devoid of tidal harmonics. The mathematical representation of the seaward boundary condition is also investigated. In the tidally-averaged Eulerian models, a fixed Dirichlet boundary condition is usually imposed, a condition that corresponds to an immediate, infinite dilution of the dissolved constituent beyond the fixed estuarine mouth. This mathematical representation of the estuarine-coastal zone interface at a fixed location is compared with the case of an oscillating location, which protrudes back and forth into the sea with the tide. Results demonstrate that the mathematical representation of the seaward boundary condition has a significant influence on the resulting mixing curves. We also show how to apply our approach to the prediction of mixing curves in real estuaries.


Dispersion Coefficient Salinity Profile Oscillatory Convection Tidal Estuary Tidal Excursion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. Bowden, K. F. 1963. The mixing processes in a tidal estuary.International Journal of Air and Water Pollution 7:343–356.Google Scholar
  2. Boyle, E., R. Collier, A. T. Dengler, J. M. Edmond, A. C. Ng, andR. F. Stallard. 1974. On the chemical mass-balance in estuaries.Geochimica Cosmochimica Acta 38:341–364.CrossRefGoogle Scholar
  3. Chatwin, P. C. andC. M. Allen. 1985. Mathematical models of dispersion in rivers and estuaries.Annual Review Fluid Mechanics 17:119–149.CrossRefGoogle Scholar
  4. Dronkers, J. 1982. Conditions for gradient-type dispersive transport in one-dimensional, tidally averaged transport models.Estuarine Coastal and Shelf Science 14:599–621.CrossRefGoogle Scholar
  5. Dronkers, J. andJ. van de Kreeke. 1986. Experimental determination of salt intrusion mechanisms in the Volkerak estuary.Netherlands Journal of Sea Research 20:1–19.CrossRefGoogle Scholar
  6. Fisher, H. B. 1972a. Mass transport mechanisms in partially stratified estuaries.Journal of Fluid Mechanics 53:671–687.CrossRefGoogle Scholar
  7. Fisher, H. B. 1972b. A Lagrangian Method for Predicting Pollutant Dispersion in Bolinas Lagoon, Marin County, California. U.S.Geological Survey Professional Paper Washington, D.C. 582-B.Google Scholar
  8. Fisher, H. B. 1976. Mixing and dispersion in estuaries.Annual Review of Fluid Mechanics 8:107–133.CrossRefGoogle Scholar
  9. Fisher, H. B., E. J. List, R. C. Y. Koh, J. Imberger, andN. H. Brooks. 1979. Mixing in Inland and Coastal Waters. Academic Press, London, U.K.Google Scholar
  10. Holley, E. R. andD. R. F. Harleman. 1965. Dispersion of Pollutants in Estuary Type Flows. Report No. 74, Hydrodynamics Laboratory. MIT, Cambridge, Massachusets.Google Scholar
  11. Hughes, F. W. andM. Rattray Jr. 1980. Salt fluxes and mixing in the Columbia River estuary.Estuarine Coastal and Marine Science 10:479–493.CrossRefGoogle Scholar
  12. Jay, D. A., R. J. Uncles, J. Largier, W. R. Geyer, J. Vallino, andW. R. Boynton. 1997. Estuarine scalar flux estimation revisited: A commentary on recent developments.Estuaries 20: 262–280.CrossRefGoogle Scholar
  13. Kaul, L. W. andP. N. Froelich. 1984. Modeling estuarine nutrient geochemistry in a simple system.Geochimica Cosmochimica Acta 48:1417–1433.CrossRefGoogle Scholar
  14. Ketchum, B. H. 1951. The exchanges of fresh and salt water in tidal estuaries.Journal of Marine Research 10:18–38.Google Scholar
  15. Ketchum, B. H. 1955. Distribution of coliform bacteria and other pollutant in tidal estuaries.Sewage and Industrial Wastes 27: 1288–1296.Google Scholar
  16. Lin, C. C. andL. A. Segel. 1988. Mathematics Applied to Deterministic Problems in the Natural Sciences. SIAM, Philadelphia, Pennsylvania.Google Scholar
  17. Liss, P. S. 1976. Conservative and non-conservative behavior of dissolved constituents during estuarine mixing, p. 93–130.In J. D. Burton and P. S. Liss (eds.), Estuarine Chemistry. Academic Press, London, U.K.Google Scholar
  18. Loder, T. C. andR. P. Reichard. 1981. The dynamics of conservative mixing in estuaries.Estuaries 4:64–69.CrossRefGoogle Scholar
  19. MacCready, P. andW. R. Geyer. 2001. Estuarine salt flux through an isohaline surface.Journal of Geophysical Research 106:11629–11637.CrossRefGoogle Scholar
  20. Neal, V. T. 1966. Predicted flushing times and pollution distribution in the Columbia river estuary, p. 1463–1480.In American Society of Civil Engineers, Proceedings of the 10th Conference of Coastal Engineers, Tokyo, Japan.Google Scholar
  21. Officer, C. B. andD. R. Lynch. 1981. Dynamics of mixing in estuaries.Estuarine Coastal Shelf Science 12:525–533.CrossRefGoogle Scholar
  22. O'Kane, J. P. 1980. Estuarine Water Quality Management. Pitman, London, U.K.Google Scholar
  23. O'Kane, J. P. andP. Regnier. 2003. A mathematically transparent low-pass filter for tidal estuaries.Estuarine Coastal and Shelf Science 57:593–603.CrossRefGoogle Scholar
  24. Pearson, C. R. andJ. R. A. Pearson. 1965. A simple method for predicting the dispersion of effluent in estuaries, p. 50–56.In Symposium No. 9: New Chemical Engineering Problems in the Utilization of Water.American Institute of Chemical Engineers, London, U.K.Google Scholar
  25. Regnier, P., A. Mouchet, R. Wollast, andF. Ronday. 1998. A discussion of methods for estimating residual fluxes in strong tidal estuaries.Continental Shelf Research 18:1543–1571.CrossRefGoogle Scholar
  26. Savenije, H. H. G. 1992. Rapid assessment techniques for salt intrusion in alluvial estuaries. Ph.D. Dissertation, IHE Delft, Delft, The Netherlands.Google Scholar
  27. Shiller, A. M. 1996. The effect of recycling traps and upwelling on estuarine chemical flux estimates.Geochimica Cosmochimica Acta 60:3177–3185.CrossRefGoogle Scholar
  28. Stommel, H. 1953. Computation of pollution in a vertically mixed estuary.Sewage Industrial Wastes 25:1061–1071.Google Scholar
  29. Thames Report. 1964. Effects of Polluting Discharges on the Thames Estuary, Water Pollution Research Technical Note No. 11. HMSO, London, U.K.Google Scholar
  30. Yeats, P. A. 1993. Input of metals to the North Atlantic from two large Canadian estuaries.Marine Chemistry 43:201–209.CrossRefGoogle Scholar

Copyright information

© Estuarine Research Federation 2004

Authors and Affiliations

  1. 1.Department of Earth Sciences-Geochemistry, Faculty of GeosciencesUtrecht UniversityUtrechtThe Netherlands
  2. 2.Department of Civil and Environmental EngineeringNational University of Ireland, Cork (UCC)CorkIreland

Personalised recommendations