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Stability Analysis of Geostrophic Adjustment on Hexagonal Grids for Regions with Variable Depth

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  • 1 Department of Mathematics, University of Bergen, Bergen, Norway
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Abstract

Hexagonal grids have been used in a number of numerical studies, and especially in relation to atmospheric models. Recent studies have suggested that ocean circulation models may also benefit from the use of hexagonal grids. These grids tend to induce less systematic errors and have better horizontal isotropy properties than traditional square grid schemes. If hexagonal grids are to be applied in ocean models, a number of features that are characteristic of ocean circulation problems need to be attended to.

The topography of the ocean basin is an important feature in most ocean models. Ocean modelers can experience instabilities due to depth variations. In the present paper, analysis of the propagation matrix for the spatially discretized system is used to explain unphysical growth of the numerical solutions of the linear shallow water equations when using hexagonal grids over domains with variable depth. It is shown that a suitable weighting of the Coriolis terms may give an energy-conserving and stable numerical scheme.

Corresponding author address: Tomas Torsvik, Dept. of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway. Email: tomast@math.uib.no

Abstract

Hexagonal grids have been used in a number of numerical studies, and especially in relation to atmospheric models. Recent studies have suggested that ocean circulation models may also benefit from the use of hexagonal grids. These grids tend to induce less systematic errors and have better horizontal isotropy properties than traditional square grid schemes. If hexagonal grids are to be applied in ocean models, a number of features that are characteristic of ocean circulation problems need to be attended to.

The topography of the ocean basin is an important feature in most ocean models. Ocean modelers can experience instabilities due to depth variations. In the present paper, analysis of the propagation matrix for the spatially discretized system is used to explain unphysical growth of the numerical solutions of the linear shallow water equations when using hexagonal grids over domains with variable depth. It is shown that a suitable weighting of the Coriolis terms may give an energy-conserving and stable numerical scheme.

Corresponding author address: Tomas Torsvik, Dept. of Mathematics, University of Bergen, Johannes Brunsgate 12, 5008 Bergen, Norway. Email: tomast@math.uib.no

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