Abstract
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.
Literature Cited
Bowden, K. F. 1963. The mixing processes in a tidal estuary.International Journal of Air and Water Pollution 7:343–356.
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.
Chatwin, P. C. andC. M. Allen. 1985. Mathematical models of dispersion in rivers and estuaries.Annual Review Fluid Mechanics 17:119–149.
Dronkers, J. 1982. Conditions for gradient-type dispersive transport in one-dimensional, tidally averaged transport models.Estuarine Coastal and Shelf Science 14:599–621.
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.
Fisher, H. B. 1972a. Mass transport mechanisms in partially stratified estuaries.Journal of Fluid Mechanics 53:671–687.
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.
Fisher, H. B. 1976. Mixing and dispersion in estuaries.Annual Review of Fluid Mechanics 8:107–133.
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.
Holley, E. R. andD. R. F. Harleman. 1965. Dispersion of Pollutants in Estuary Type Flows. Report No. 74, Hydrodynamics Laboratory. MIT, Cambridge, Massachusets.
Hughes, F. W. andM. Rattray Jr. 1980. Salt fluxes and mixing in the Columbia River estuary.Estuarine Coastal and Marine Science 10:479–493.
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.
Kaul, L. W. andP. N. Froelich. 1984. Modeling estuarine nutrient geochemistry in a simple system.Geochimica Cosmochimica Acta 48:1417–1433.
Ketchum, B. H. 1951. The exchanges of fresh and salt water in tidal estuaries.Journal of Marine Research 10:18–38.
Ketchum, B. H. 1955. Distribution of coliform bacteria and other pollutant in tidal estuaries.Sewage and Industrial Wastes 27: 1288–1296.
Lin, C. C. andL. A. Segel. 1988. Mathematics Applied to Deterministic Problems in the Natural Sciences. SIAM, Philadelphia, Pennsylvania.
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.
Loder, T. C. andR. P. Reichard. 1981. The dynamics of conservative mixing in estuaries.Estuaries 4:64–69.
MacCready, P. andW. R. Geyer. 2001. Estuarine salt flux through an isohaline surface.Journal of Geophysical Research 106:11629–11637.
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.
Officer, C. B. andD. R. Lynch. 1981. Dynamics of mixing in estuaries.Estuarine Coastal Shelf Science 12:525–533.
O'Kane, J. P. 1980. Estuarine Water Quality Management. Pitman, London, U.K.
O'Kane, J. P. andP. Regnier. 2003. A mathematically transparent low-pass filter for tidal estuaries.Estuarine Coastal and Shelf Science 57:593–603.
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.
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.
Savenije, H. H. G. 1992. Rapid assessment techniques for salt intrusion in alluvial estuaries. Ph.D. Dissertation, IHE Delft, Delft, The Netherlands.
Shiller, A. M. 1996. The effect of recycling traps and upwelling on estuarine chemical flux estimates.Geochimica Cosmochimica Acta 60:3177–3185.
Stommel, H. 1953. Computation of pollution in a vertically mixed estuary.Sewage Industrial Wastes 25:1061–1071.
Thames Report. 1964. Effects of Polluting Discharges on the Thames Estuary, Water Pollution Research Technical Note No. 11. HMSO, London, U.K.
Yeats, P. A. 1993. Input of metals to the North Atlantic from two large Canadian estuaries.Marine Chemistry 43:201–209.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Regnier, P., O'Kane, J.P. On the mixing processes in estuaries: The fractional freshwater method revisited. Estuaries 27, 571–582 (2004). https://doi.org/10.1007/BF02907645
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02907645