The Application of Curvilinear Coordinate for Primitive Equation in the Gulf of Thailand

W. Wannawong, U. Humphries, A. Luadsong


The curvilinear grid is mapped onto a place in which the irregular basin is transformed into a series of connected rectangles. An equispaced grid is used in the connected rectangle system, and all the calculations are conveniently performed in this system. The advantage of such a grid is that the boundary of the water body always falls on a coordinate line and the grid points are closely spaced in the narrow and shallow areas. In this paper, we modify the Princeton Oceanic Model (POM) to study the formulations and its applications of the primitive equations that are generated to the orthogonal curvilinear coordinate (OCC) system and used for the horizontal coordinates in a three-dimensional circulation model. The area of the study covers from 98.54 $^\circ$E to 105. 54$^\circ$E in longitude and 5.54$^\circ$N to 14.54$^\circ$N in latitude. In addition, we also study the pressure gradient error (PGE) tested with both of the OCC grids and orthogonal rectangular coordinate (ORC) grids. The resolution grid points of the OCC and ORC grids have the same number of $37 \times 97$ in longitude (E ) and latitude (N ), respectively. Thevertical resolution is 10 vertical levels. The result of the study indicate that the actual flow is produced directly by wind forcing induced the circulation inside the Gulf of Thailand (GoT) characterized by the migration of water from the southeast to the north of the GoT. Using of the OCC system has made possible high resolution required without paying the penalty imposed by unnecessary high resolutionin other parts of the region. Furthermore, the comparison of the averaged velocity induced by the PGE between the OCC and ORC grids with the same number of grid points show that the OCC grids are more efficient for the GoT than the rectangular grids. The OCC grids are very useful for description about the circulation in the coastal ocean modeling, especially a coastal region in theGoT with complex coastlines and the steepness of topography.

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The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

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|ISSN 1686-0209|