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Fundamentals of Estuarine Physical Oceanography pp 233–282Cite as

Hydrodynamic Formulation: Mass and Salt Conservation Equations

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Part of the book series: Ocean Engineering & Oceanography ((OEO,volume 8))

Abstract

When hydrographic properties and motions in an estuary have spatial and temporal variation, they are termed as non-uniform and unsteady, as opposed to uniform and in steady-state.

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Notes

  1. 1.

    The dynamic coefficients of eddy diffusion (dispersion), Ax, Ay and Az, which have dimensions of [ML−1T−1], is obtained from the product of density, ρ, by the corresponding kinematic coefficient; Ax = ρKx, Ay = ρKy and Az = ρKz.

  2. 2.

    When the estuary bottom is plane (H0 = const.), and due to the very long tidal wave, the tidal elevation may be considered uniform along the estuary, η = η(t), and it is possible to change the order of the integral operator and the derivative. In these conditions w|−H0 = 0 and w|η = dη/dt = ∂η/∂t are the kinematic boundary conditions.

  3. 3.

    This operation is equivalent to the Mean Value Theorem.

  4. 4.

    This type of estuary is usually shallow and the influence of the gravitational circulation may be disregarded and the baroclinic bumping landward is negligible.

References

  • Arons, A. B. & Stommel, H. 1951. “A Mixing-Length Theory of Tidal Flushing”. Trans. Am. Geophys.Un., 32(3):419–421.

    Google Scholar 

  • Blumberg, A. F. 1975. A Numerical Investigation into the Dynamics of Estuarine Circulation. Tech. Rept. Chesapeake Bay Institute, The Johns Hopkins University. n. 91. 110 p. + Apêndices.

    Google Scholar 

  • Bowden, K. F. 1963. The Mixing Processes in a Tidal Estuary. J. Air Wat. Pollut., 7:343‑356.

    Google Scholar 

  • Brand, L. 1959. Análisis Vectorial. Compania Editorial Continental, S.A., 333 p.

    Google Scholar 

  • Cameron, W. M. & Pritchard, D. W. 1963. “Estuaries”. In: Hill, M. N. (ed.). The Sea. Ideas and Observations on Progress in the Study of the Seas. New York, Interscience, pp. 306–324.

    Google Scholar 

  • Csanady, G. T. 1982. Circulation in the Coastal Ocean. D. Reidel Publishing, Dordrecht, 279 p. (Environmental Fluid Mechanics).

    Google Scholar 

  • Defant, A. 1961. Physical Oceanography. Oxford, Pergamon Press, vol. 1. 729 p.

    Google Scholar 

  • Dyer, K. R. 1973. Estuaries: A Physical Introduction. London, Wiley. 140 p.

    Google Scholar 

  • Fisher, J. S.; Ditmars, J. D. & Ippen, A. T. 1972. Mathematical Simulation of Tidal‑Time Averages of Salinity and Velocity Profiles in Estuaries. Massachusetts Institute of Technology, Mass., Rept. MITSG 72–11, 157 p.

    Google Scholar 

  • Fischer, H. B.; List, E. J.; Koh, R. C. Y.; Imberger, J. & Brooks, N. H. 1979. Mixing in Inland and Coastal Waters. New York, Academic Press. 483 p.

    Google Scholar 

  • Geyer, W.R. 2010. Estuarine salinity structure and circulation. In: ed. Valle-Levinson A. Contemporary Issues in Estuarine Physics. Cambridge University Press, pp. 12–26.

    Google Scholar 

  • Geyer, W. R. & Farmer, D. M. 1989. Tide-Induced Variations of the Dynamics of a Salt Wedge Estuary. J. Phys. Oceanogr., v.19, pp. 1060–1072.

    Google Scholar 

  • Gill, A. E. 1982. Atmospheric-Ocean Dynamics. New York, Academic Press. 662 p.

    Google Scholar 

  • Hansen, D. V. & Rattray Jr., M. 1965. Gravitational Circulation in Sraits and Estuaries. J. Mar. Res., 23(1):102–122.

    Google Scholar 

  • Ketchum, B. H. 1955. Distribution of Coliform Bacteria and other Pollutants in Tidal Estuaries. Sew. Ind. Wastes, 27:1288–1296.

    Google Scholar 

  • Kinsman, B. 1965. Wind Waves-Their Generation and Propagation on the Ocean Surface. New Jersey, Prentice-Hall. 676 p.

    Google Scholar 

  • Lacombe, H. 1965. Cours d’Océanographie Physique (Théories de la circulation générale. Houles et vagues). Paris, Gauthiers-Villars. 392 p.

    Google Scholar 

  • Maximon, L. C. & Morgan, G. W. 1955. A Theory of Tidal Mixing in a Vertically Homogeneous Estuary. J. Mar. Res., 14:157–175.

    Google Scholar 

  • Neumann, G. & Pierson, W. J. Jr. 1966. Principles of Physical Oceanography. London, Prentice-Hall. 545 p.

    Google Scholar 

  • Officer, C. B. 1976. Physical Oceanography of Estuaries (and Associated Coastal Waters). New York, Wiley. 465 p.

    Google Scholar 

  • Officer, C. B. 1977. Longitudinal Circulation and Mixing Relations in Estuaries. Estuaries, Geophysics, and the Environment. Washington, D. C., National Academy of Sciences, pp. 13–21.

    Google Scholar 

  • Officer, C. B. 1978. Some Simplified Tidal Mixing and Circulation Flux Effects in Estuaries. In: Kjerfve, B. (ed.). Estuarine Transport Processes. Columbia, University of South Carolina Press, pp. 75–93 (The Belle W. Baruch Library in Marine Science, 7).

    Google Scholar 

  • Okubo, A. 1964. Equations Describing the Diffusion of an Introduced Pollutant in a One-dimensional Estuary. In: Yoshida, K. (ed.). Studies on Oceanography. Tokyo, University of Tokyo Press, pp. 216–226.

    Google Scholar 

  • Pritchard, D.W. 1954. A Study of Salt Balance in a Coastal Plain Estuary. J. Mar. Res., 13(1):133‑144.

    Google Scholar 

  • Pritchard, D. W. 1955. Estuarine Circulation Patterns. Proc. Am. Soc. Civ. Eng., 81:717:1–11.

    Google Scholar 

  • Pritchard, D. W. 1958. The Equations of Mass Continuity and Salt Continuity in Estuaries. J. Mar. Res., 17:412–423.

    Google Scholar 

  • Pritchard, D. W & Kent, R. E. 1956. A Method of Determining Mean Longitudinal Velocities in a Coastal Plain Estuary. J. Mar. Res., 15(1):81–91.

    Google Scholar 

  • Rattray Jr., M. & Hansen, D. V. 1962. A Similarity Solution for Circulation in an Estuary. J. Mar. Res., 20(2):121–133.

    Google Scholar 

  • Severi, F. 1956. Lecciones de Análisis. Barcelona, Labor, v. 2. 429 p.

    Google Scholar 

  • Stommel, H. 1953a. The Role of Density Currents in Estuaries. Proc. Minnesota International Hydraulics Convention, Minneapolis, University of Minnesota, pp. 305–312.

    Google Scholar 

  • Stommel, H. 1953b. Computation of Pollution in a Vertically Mixed Estuary. Sew. Ind. Wastes, 25(9):1065–1071.

    Google Scholar 

  • Svedrup, H. U.; Johnson, M. W. & Fleming, R. H. 1942. The Oceans, their Physics, Chemistry and General Biology. New Jersey, Prentice-Hall. 1042 p.

    Google Scholar 

  • Symon, K. R. 1957. Mechanics. Addison-Wesley Publishing Company, Inc., sec. ed. 358 p.

    Google Scholar 

  • Team Course. 2001. Ocean Circulation. Oxford, Open University Course Team/Pergamon Press. 2nd. Edition 286 p.

    Google Scholar 

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Authors and Affiliations

  1. Oceanographic Institute, University of São Paulo (IOUSP), São Paulo, Brazil

    Luiz Bruner de Miranda & Belmiro Mendes de Castro Filho

  2. Griffith Climate Change Response Program (GCCRP), Griffith Centre for Coastal Management (GCCM), Griffith School of Engineering, Gold Coast, QLD, Australia

    Fernando Pinheiro Andutta

  3. American University of Sharjah, Sharjah, United Arab Emirates

    Björn Kjerfve

Authors
  1. Luiz Bruner de Miranda
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  2. Fernando Pinheiro Andutta
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  3. Björn Kjerfve
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  4. Belmiro Mendes de Castro Filho
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Correspondence to Fernando Pinheiro Andutta .

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Bruner de Miranda, L., Andutta, F.P., Kjerfve, B., de Castro Filho, B.M. (2017). Hydrodynamic Formulation: Mass and Salt Conservation Equations. In: Fundamentals of Estuarine Physical Oceanography. Ocean Engineering & Oceanography, vol 8. Springer, Singapore. https://doi.org/10.1007/978-981-10-3041-3_7

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  • DOI: https://doi.org/10.1007/978-981-10-3041-3_7

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