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The Open Boundary Equation : Volume 12, Issue 3 (01/06/2015)

By Diederen, D.

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Book Id: WPLBN0004020905
Format Type: PDF Article :
File Size: Pages 34
Reproduction Date: 2015

Title: The Open Boundary Equation : Volume 12, Issue 3 (01/06/2015)  
Author: Diederen, D.
Volume: Vol. 12, Issue 3
Language: English
Subject: Science, Ocean, Science
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Historic
Publication Date:
2015
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Toffolon, M., G. Savenij, H. H., & Diederen, D. (2015). The Open Boundary Equation : Volume 12, Issue 3 (01/06/2015). Retrieved from http://worldlibrary.net/


Description
Description: Department of Water Management, Delft University of Technology, Delft, the Netherlands. We present a new equation describing the hydrodynamics in infinitely long tidal channels (i.e., no reflection) under the influence of oceanic forcing. The proposed equation is a simple relationship between partial derivatives of water level and velocity. It is formally derived for a progressive wave in a frictionless, prismatic, tidal channel with a horizontal bed. Assessment of a large number of numerical simulations, where an open boundary condition is posed at a certain distance landward, suggests that it can also be considered accurate in the more natural case of converging estuaries with nonlinear friction and a bed slope. The equation follows from the open boundary condition and is therefore a part of the problem formulation for an infinite tidal channel. This finding provides a practical tool for evaluating tidal wave dynamics, by reconstructing the temporal variation of the velocity based on local observations of the water level, providing a fully local open boundary condition and allowing for local friction calibration.

Summary
The open boundary equation

Excerpt
Cai, H. and Savenije, H. H. G.: Asymptotic behavior of tidal damping in alluvial estuaries, J. Geophys. Res.-Oceans, 118, 6107–6122, doi:10.1002/2013JC008772, 2013.; Cai, H., Savenije, H. H. G., and Toffolon, M.: A new analytical framework for assessing the effect of sea-level rise and dredging on tidal damping in estuaries, J. Geophys. Res.-Oceans, 117, C09023, doi:10.1029/2012JC008000, 2012.; Cai, H., Savenije, H. H. G., and Toffolon, M.: Linking the river to the estuary: influence of river discharge on tidal damping, Hydrol. Earth Syst. Sci., 18, 287–304, doi:10.5194/hess-18-287-2014, 2014.; De Saint-Venant, A. J. C. B.: Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et à l'introduction de marées dans leurs lits, Comptes rendus des séances de l`Académie des Sciences, 73, 237–240, 1871.; Engquist, B. and Majda, A.: Absorbing boundary conditions for the numerical simulation of waves, Math. Comput., 31, 629–651, doi:10.1090/S0025-5718-1977-0436612-4, 1977.; Friedrichs, C. T. and Aubrey, D. G.: Tidal propagation in strongly convergent channels, J. Geophys. Res.-Oceans, 99, 3321–3336, doi:10.1029/93JC03219, 1994.; Hunt, J. N.: Tidal oscillations in estuaries, Geophys. J. Roy. Astr. S., 8, 440–455, doi:10.1111/j.1365-246X.1964.tb03863.x, 1964.; Jay, D. A.: Green's law revisited: tidal long-wave propagation in channels with strong topography, J. Geophys. Res.-Oceans, 96, 20585–20598, doi:10.1029/91JC01633, 1991.; Keller, J. B. and Voli, D.: Exact non-reflecting boundary conditions, J. Comput. Phys., 82, 172–192, doi:10.1016/0021-9991(89)90041-7, 1989.; Orlanski, I.: A simple boundary condition for unbounded hyperbolic flows, J. Comput. Phys., 21, 251–269, doi:10.1016/0021-9991(76)90023-1, 1976.; Riemann, G. F. B.: Über die Fortpflanzung ebener Luftwellen von endlicher Schwingungsweite, Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, 8 , 43–65, 1859.; Savenije, H. H. G.: Lagrangian solution of St. Venant's equations for an alluvial estuary, J. Hydraul. Eng., 118, 1153–1163, doi:10.1061/(ASCE)0733-9429(1992)118:8(1153), 1992.; Savenije, H. H. G.: Salinity and Tides in Alluvial Estuaries, Elsevier, Amsterdam, 2005.; Savenije, H. H. G.: Salinity and Tides in Alluvial Estuaries, 2nd revised edn., available at: www.salinityandtides.com (last access: 26 May 2015), Delft, the Netherlands, 2012.; Savenije, H. H. G., Toffolon, M., Haas, J., and Veling, E. J. M.: Analytical description of tidal dynamics in convergent estuaries, J. Geophys. Res.-Oceans, 113, C10025, doi:10.1029/2007JC004408, 2008.; Toffolon, M. and Savenije, H. H. G.: Revisiting linearized one-dimensional tidal propagation, J. Geophys. Res.-Oceans, 116, C07007, doi:10.1029/2010JC006616, 2011.; Toffolon, M., Vignoli, G., and Tubino, M.: Relevant parameters and finite amplitude effects in estuarine hydrodynamics, J. Geophys. Res.-Oceans, 111, C10014, doi:10.1029/2005JC003104, 2006.

 

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