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A Transformed Coordinates Shallow Water Model for the Head of the Bay of Bengal Using Boundary-Fitted Curvilinear Grids

Published online by Cambridge University Press:  28 May 2015

Farzana Hussain
Farzana Hussain*
Affiliation:
Department of Mathematics, Shahjalal University of Science & Technology, Sylhet, Bangladesh
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Abstract

The Bay of Bengal is surrounded by coastline except to the south, where there is open sea. The coastline bends most sharply along the coast of Bangladesh, and there are many small and large islands in the off shore region there. In order to incorporate the island boundaries and the curved coastline properly, in any numerical scheme it is often necessary to consider a very fine grid resolution along the coastal belts whereas this is unnecessary away from the coasts. However, a very fine resolution involves more memory and more CPU time in the numerical solution process, and invites numerical instability. On the other hand, boundary-fitted curvilinear grids in hydrodynamic models for coastal seas, bays and estuaries not only fit to the coastline but also render the finite difference schemes simpler and more accurate. In this article, the boundary-fitted curvilinear grids for the model represent the complete boundary of the area considered by four curves defined by four functions, and the four boundaries of two of the larger islands are then represented approximately by two general functions. An appropriate independent coordinate transformation maps the curvilinear physical area to a square domain, and each island boundary is transformed to a rectangle within this square domain. The vertically integrated shallow water equations are transformed to the new space domain, and solved by a regular explicit finite difference scheme. The model is applied to compute the water levels due to astronomical tides, and also the water levels due to surges associated with tropical storms that hit the coast of Bangladesh.

Keywords

35F3037M0565N0665N2265N50Tropical stormssurgetide generationshallow water equationsboundary-fitted gridsBay of Bengal
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 3 , Issue 1 , February 2013 , pp. 27 - 47
Copyright
Copyright © Global-Science Press 2013

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References

[1]Das, P. K. (1972) Prediction model for storm surges in the Bay of Bengal. Nature 239, 211–213.Google Scholar
[2]Flierl, G. R. and Robinson, A. R. (1972) Deadly surges in the Bay of Bengal: Dynamics and storm tide tables. Nature 239, 213–215.Google Scholar
[3]Das, P. K., Sinha, M. C. and Balasubrahmanyam, V. (1974) Storm surges in the Bay of Bengal. Quart J. Roy. Met. Soc. 100, 437–449.Google Scholar
[4]Johns, B. and Ali, A. (1980) The numerical modeling of storm surges in the Bay of Bengal. Quart. J. Roy. Met. Soc. 106, 1–18.Google Scholar
[5]Dube, S. K., Sinha, P. C. and Roy, G. D. (1985) The numerical simulation of storm surges along the Bangladesh coast. Dynam. Atmos. Oceans 9, 121–133.CrossRefGoogle Scholar
[6]Dube, S. K., Sinha, P. C. and Roy, G. D. (1986) The numerical simulation of storm surges in Bangladesh using a bay-river coupled model. Coast Eng. 10, 85–101.Google Scholar
[7]Johns, B., Dube, S. K., Mohanti, U. C. and Sinha, P. C. (1981) Numerical simulation of surge generated by the 1977 Andhra cyclone. Quart. J. Roy. Soc. London 107, 919–934.Google Scholar
[8]Johns, B., Dube, S. K., Mohanti, U. C. and Sinha, P. C. (1982) The simulation of continuously deforming lateral boundary in problems involving the shallow water equations. Comput. Fluids 10, 105–116.CrossRefGoogle Scholar
[9]Johns, B., Rao, A. D., Dube, S. K. and Sinha, P. C. (1985) Numerical modeling of tide-surges interaction in the Bay of Bengal. Phil. Trans. R. Soc. London A 313, 507–535.Google Scholar
[10]Sinha, P. C., Dube, S. K. and Roy, G. D. (1986) Numerical simulation of storm surges in Bangladesh using a multi-level model. Int. J. Num. Methods Fluids 6, 305–311.Google Scholar
[11]Roy, G. D. (1985) Some aspects of storm surges along the coast of Bangladesh. Ganith - J. Bangladesh Math. Soc. 6(1), 1–8.Google Scholar
[12]Roy, G. D. (1995) Estimation of expected maximum possible water level along the Meghna estuary using a tide and surge interaction model. Environ. Int. 21(5), 671–677.Google Scholar
[13]Roy, G. D. (1999) Inclusion of offshore islands in transformed coordinates shallow water model along the coast of Bangladesh. Environ. Int. 25(1), 67–74.Google Scholar
[14]Jelesnianski, C. P. (1965) A numerical calculation of storm tides induced by a tropical storm impinging on a continental self. Mon. Wea. Rev. 93, 343–358.2.3.CO;2>CrossRefGoogle Scholar
[15]Johnson, B. H. (1982) Numerical modeling of estuarine hydrodynamics on a boundary fitted coordinate system. In Numerical Grid Generation (Thompson, J. ed.) Elsevier Science, 419–436.Google Scholar
[16]Spaulding, M. L. (1984) A vertical averaged circulation model using boundary-fitted coordinates. J. Phys. Oceanogr. 14, 973–982.Google Scholar
[17]Sheng, Y. P. (1989) On modeling three-dimensional estuarine and marine hydrodynamics. In Three-dimensional Models of Marine and Estuarine Dynamics (Nihoul, J. C. J. and Jamart, B. M. ed.) Elsevier Oceanography, Series 45, 35–54.Google Scholar
[18]Androsov, A. A., Vol'tzinger, N. E. and Liberman, Y. M. (1997) A two dimensional tidal model of the Barents Sea. Oceanology 37, 16–22.Google Scholar
[19]Bao, X. W., Yan, J. and Sun, W. X. (2000) A three-dimensional tidal model in boundary-fitted curvilinear grids. Estuar. Coast. Shelf Sci. 50, 775–788.CrossRefGoogle Scholar