Nested numerical scheme in a polar coordinate shallow water model for the coast of Bangladesh
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Nested numerical scheme in a polar coordinate shallow water model for the coast of Bangladesh M. Mizanur Rahman & Gour Chandra Paul & Ashabul Hoque
Received: 15 December 2011 / Revised: 25 July 2012 / Accepted: 3 September 2012 / Published online: 16 September 2012 # Springer Science+Business Media B.V. 2012
Abstract This study is concerned with the development of storm surge model to predict water level accurately due to surge associated with a cyclone along the coast of Bangladesh. Considering the funnel shape of the Bay of Bengal, coastal bending and the existence of offshore islands, a vertically integrated model in cylindrical polar coordinate system is developed using nested numerical scheme. A fine mesh scheme capable of incorporating coastal bending and offshore islands properly in the numerical scheme is nested into a coarse mesh scheme covering up to 15° N latitude of the Bay of Bengal. The developed model is used to estimate water levels at different coastal and island stations associated with a few storms that hit the coast of Bangladesh. The computed surge levels compared well with observed ones and predicted surge levels investigated with different approaches. Keywords Bay of Bengal . Shallow water model . Cylindrical polar coordinates . Finite difference method . Water level
M. M. Rahman (*) Department of Mathematics, Shahjalal University of Science & Technology, Sylhet 3114, Bangladesh e-mail: [email protected] G. C. Paul : A. Hoque Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh Present Address: M. M. Rahman Department of Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh
Introduction Among all the natural calamities, tropical storms along with tidal surges are the most devastating in nature along the coast of Bangladesh. During storm surges, the sea level rises abnormally due to the strong circulatory wind associated with a tropical storm. The surges develop the form of long waves and approach the coast with considerable phase speed approximately defined by pffiffiffiffiffi gh, where g is the acceleration due to gravity and h is the water depth. Both tropical storms and the associated surges cause tremendous devastation when they approach the coast. Frank and Husain (1971) showed that the major cause of damage is due to the associated surges rather than the storm itself. According to their estimation about 90 % of marine fishermen suffered casualties and about 65 % of total annual fishing capacity of coastal areas were destroyed in November 1970 storm that hit the coast of Bangladesh. The shape and structure of the Bangladesh coastline, shallowness of water, offshore islands, the huge discharge from the Meghna basin and low lying coastal areas make it vulnerable for high surge even with a storm of low intensity. There had been a large volume of works done for the Bay of Bengal on the analysis and prediction of tide, surge and their interaction including some of the previously mentioned factors (see e.g., Das 1972; Das et al. 1974; Flierl and Robinson 1972; J
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