On the Use of the Sigma-coordinate System in Regions of Large Bathymetric Variations

Deleersnijder, Eric;Beckers, JM.
(1992) Journal of Marine Systems — Vol. 3, n° 4-5, p. 381-390 (1992)

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Abstract
The sigma-transformation is a widely used coordinate change that maps the actual depth-varying sea onto a computational domain, the depth of which is constant. The advantages of this technique are numerous. It permits an efficient use of computer resources, a simple treatment of the surface and bottom boundary conditions, and an accurate representation of the bathymetry. However, if the range of the depth is too large, or when the depth varies too rapidly, as in the shelf break region, it may be shown that the sigma-transformation leads to severe numerical errors. In the application of GHER's three-dimensional model to the Western Mediterranean, the occurrence of those numerical errors is avoided by the introduction of a two-fold sigma-coordinate system in the deep sea.
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Deleersnijder, E., & Beckers, JM. (1992). On the Use of the Sigma-coordinate System in Regions of Large Bathymetric Variations. Journal of Marine Systems, 3(4-5), 381-390. https://doi.org/10.1016/0924-7963(92)90011-V (Original work published 1992)