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Fundamentals of Estuarine Physical Oceanography pp 283–326Cite as

Hydrodynamic Formulation: Equations of Motion and Applications

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

Abstract

Estuarine hydro- and thermodynamics processes control a variety of physical phenomena which are described by the water level, field of motion (tidal currents and gravitational circulation), and hydrographic properties (salinity, temperature, pressure).

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Notes

  1. 1.

    This velocity profile is equal to the one obtained by Officer (1978) with the Oz axis also oriented against the gravity acceleration, but with its origin at the free surface.

  2. 2.

    For a frictionless estuary the order of magnitude of U0 may be estimated by Eq. (2.24a, b, Chap. 2).

  3. 3.

    If the advective acceleration is disregarded and, η ≪ H0, this system of equations is reduced to the Eqs. (2.14) and (2.17) (Chap. 2).

References

  • 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. 1953. Note on Wind Drift in a Channel in the Presence of Tidal Currents. Proc. R. Soc. Lond., A219, pp. 426–446.

    Google Scholar 

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

    Google Scholar 

  • Bowden, K. F. 1967b. Stability effects on turbulent mixing in tidal currents. Phys. Fluid. 10 (suppl), S278-S280.

    Google Scholar 

  • Bowden, K. F. & Fairbairn, L.A. 1952. A Determination of the Frictional Forces in a Tidal Current. Proc. Royal.Soc. Lond. A, 214. p. 371–392.

    Google Scholar 

  • Chant, R.J. 2010. Estuary secondary circulation. In: ed. Valle-Levinson A. Contemporary Issues in Estuarine Physics. Cambridge University Press, pp. 100–124.

    Google Scholar 

  • Charnock, H. 1981. Air-sea Interaction. In: Warren, B. A. & Wunsch, C. (eds.). Evolution of Physical Oceanography. Cambridge, MIT Press, pp. 482–503.

    Google Scholar 

  • Ferraz, L. A. de C. 1975. Tidal and Current Prediction for the Amazon’s North Channel using a Hydrodynamical-Numerical Model. M. Sc. Dissertation. California, Naval Post-graduate School. 85 p.

    Google Scholar 

  • Franco, A. S. 1988. Tides: Fundamentals, Analysis and Prediction. São Paulo, Fundação Centro Tecnológico de Hidráulica. 249 p.

    Google Scholar 

  • Franco, A. S. 2009. Marés – Fundamentos, Análise e Previsão. Diretoria de Hidrografia e Navegação. Rio de Janeiro, 2nd ed., 344 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 

  • 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 

  • Geyer, W. R. 1997. Influence of Wind on Dynamics and Flushing of Shallow Estuaries. Estuar. Coast. Shelf Sci., 44:713–722.

    Google Scholar 

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

    Google Scholar 

  • Hamilton, P. & Rattray Jr., M. 1978. Theoretical Aspects of Estuarine Circulation. In: Kjerfve B. (ed.). Estuarine Transport Processes. Columbia, University of South Carolina, pp. 37–73. (Belle W. Baruch Library in Marine Science, 7).

    Google Scholar 

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

    Google Scholar 

  • Hansen, D. V. & Rattray Jr., M. 1966. New Dimensions in Estuary Classification. Limnol. Oceanogr., 11(3):319–325.

    Google Scholar 

  • Harari, J. & Camargo, R. 1998. Modelagem Numérica da Região Costeira de Santos (SP): Circulação de Maré. Rev. Bras. Oceanogr., São Paulo, 46(2):135–156.

    Google Scholar 

  • Harleman, D. R. F. & Ippen, A. T. 1967. Two-Dimensional Aspects of Salinity Intrusion in Estuaries: Analysis and Velocity Distributions. Committee on Tidal Hydraulics. Tech. Bull., Corps of Engineers, U. S. Army, n. 13.

    Google Scholar 

  • Ianniello, J. P. 1977. Tidally induced residual currents in estuaries of constant breadth and depth. Journal of Marine Research, 35(4), 755–786.

    Google Scholar 

  • Ianniello, J. P. 1979. Tidally induced residual currents in estuaries of variable breadth and depth. J. Phys. Oceanogr., 9, 962–974.

    Google Scholar 

  • Ippen, A. T. & Harleman, D. R. F. 1961. One-Dimensional Analysis of Salinity Intrusion in Estuaries. Committee on Tidal Hydraulics. Tech. Bull. Corps of Engineers U. S. Army, n. 5. 120 p.

    Google Scholar 

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

    Google Scholar 

  • King B. & Wolanski, E. 1996. Bottom Friction Reduction in Turbid Estuaries. In: ed. Pattiaratchi C., Coastal and Estuarine: Mixing in Estuaries and Coastal Seas. American Geophysical Union, pp. 325:337.

    Google Scholar 

  • Kjerfve, B. & Ferreira, H. O. 1993. Tidal Bores: First Ever Measurements. Ciência Cult., São Paulo, 45(2):135–137.

    Google Scholar 

  • Kjerfve, B.; Miranda, L. B. & Wolanski, E. 1991. Modelling Water Circulation in an Estuary and Intertidal Salt Marsh System. Neth. J. Sea Res., 28(3):141–147.

    Google Scholar 

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

    Google Scholar 

  • Lessa, G. 1996. Tidal Dynamics and Sediment Transport in a Shallow Macrotidal Estuary. In: ed. Pattiaratchi C., Coastal and Estuarine: Mixing in Estuaries and Coastal Seas. American Geophysical Union, pp. 338:360.

    Google Scholar 

  • Liu, W. T.; Katsaros, K. B. & Businger, J. A. 1979. Bulk Parametrisation of Air-Sea Exchanges of Heat and Water Vapour Including Molecular Constraints at the Interface. J. Atmos. Sci., 36:1722–1735.

    Google Scholar 

  • Miranda, L. B.; Dalle Olle, E.; Bérgamo, A.L.; Silva, L.S. & Andutta, F.P. 2012. Circulation and salt intrusion in the Piaçaguera Channel, Santos (SP). Braz. J. Oceanography, 60(1):11–23.

    Google Scholar 

  • Möller, O. O. Jr., 1996. Hydrodynamique de la Lagune dos Patos (30oS, Brésil). Mesures et Modélisation. Tese de Doutorado. Bordeaux, L’Université de Bordeaux I. École Doctorale des Sciences de la Terre et de la Mer. 204 p.

    Google Scholar 

  • Munk, W. H. & Anderson E. R. Anderson 1948. Notes on the theory of the thermocline, J. Mar. Res., 3, 276–295, 1948

    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 

  • Paiva, A. M. & Rosman, P. C. C. 1993. Modelagem Numérica de Circulação em Estuários Estratificados. X Simpósio Brasileiro de Recursos Hídricos – I Simpósio de Recursos Hídricos do Cone Sul. ABRH, Rio de Janeiro, vol. 5, pp. 485–494.

    Google Scholar 

  • Pedloski, J. 1979. Geophysical Fluid Dynamics. 2. ed., New York, Springer-Verlag. 624 p.

    Google Scholar 

  • Prandle, D. 1982. The Vertical Structure of Tidal Currents and other Oscillatory Flows. Continent. Shelf Res., 1(2):191–207.

    Google Scholar 

  • Prandle, D. 1985. On Salinity Regimes and the Vertical Structure of Residual Flows in Narrow Tidal Estuaries. Estuar. Coast. Shelf Sci., 20:615–635.

    Google Scholar 

  • Prandle, D. 2004. Saline Intrusion in Partially Mixed Estuaries. Est. Coast. Shelf Sci. (59):385–397.

    Google Scholar 

  • Prandle, D. 2009. Estuaries: Dynamics, Mixing, Sedimentation and Morphology. Cambridge University Press, N.Y., 236 p.

    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. 1956. The Dynamic Structure of a Coastal Plain Estuary. J. Mar. Res., 15(1):33–42.

    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. 1971. Two-Dimensional Models. In: Ward Jr., G. H. & Espey Jr., W. H. (eds.). Estuarine Modelling: An Assessment Capabilities and Limitations for Resource Management and Pollution Control. Austin, Tracor, pp. 22–33. (Water Pollution Control Research Series).

    Google Scholar 

  • Pugh, D. T. 1987. Tides, Surges and Mean Sea-Level, Wiley, New York.

    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 

  • Roll, H. U. 1965. Physics of the Marine Atmosphere. New York, Academic Press. 497 p. (International Geophysics Series, 7).

    Google Scholar 

  • Simpson, J. H.; Brown, J.; Mattews, J. & Allen, G. 1990. Tidal Straining, Density Currents, and Stirring in the Control of Estuarine Stratification. Estuaries, 13(2), p. 125–132.

    Google Scholar 

  • Smith, S. D. 1980. Wind Stress and Heat Flux over the Ocean in Gale Force Winds. J. Phys. Oceanogr., 10:709–726.

    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 

  • 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 

  • Thatcher, M. L. & Harleman, D. R. F. 1972. Prediction of Unsteady Salinity Intrusion in Estuaries: Mathematical Model and User’s Manual. Massachusetts Institute of Technology, Mass., Rep. MITSG 72–21. 193 p.

    Google Scholar 

  • Wolanski, E.; Jones, M. & Bunt, J. S. 1980. Hydrodynamics of a Tidal Creek-Mangrove Swamp System. Aust. J. Mar. Freshwat. Res., 31:431–450.

    Google Scholar 

  • Wolanski, E.; King, B. & Galloway, D. 1997. Salinity Intrusion in The Fly River Estuary, Papua New Guinea. J. Coast. Res., 13(4):983–994.

    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

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  1. Luiz Bruner de Miranda
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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: Equations of Motion and Applications. In: Fundamentals of Estuarine Physical Oceanography. Ocean Engineering & Oceanography, vol 8. Springer, Singapore. https://doi.org/10.1007/978-981-10-3041-3_8

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