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Geostrophic Adjustment on Hexagonal Grids

Slobodan NičkovićEuro–Mediterranean Centre on Insular Coastal Dynamics, Foundation for International Studies, University of Malta, Valletta, Malta

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Milivoj B. GavrilovVojvodina, Serbia

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Ivana A. TošićInstitute of Meteorology, University of Belgrade, Belgrade, Serbia

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Abstract

A simple two-dimensional linearized model of the atmosphere is used to investigate behavior of the geostrophic adjustment process on five selected horizontal hexagonal grids. This study shows that hexagonal lattices have some advantages over commonly used square grids. Having better isotropy, they provide more accurate dispersion of gravity waves than square grids do, and therefore they can be more appropriate for simulation of smaller-scale divergent processes. The gravity–inertia wave frequencies of most of the considered grids are also closer to the true solution than those on square grids. However, some hexagonal grids are not completely free of numerical inconsistencies. For example, one of the selected grids generates nonsymmetric roots of the gravity–inertia solution that may lead to the unwanted simulation of the atmospheric process. The analysis indicates which hexagonal distributions can be an appropriate choice for use in atmospheric and ocean models.

Corresponding author address: Slobodan Ničković, Euro-Mediterranean Centre on Insular Coastal Dynamics, Foundation for International Studies, University of Malta, St. Paul Street, Valletta, Malta. Email: nicko@icod.org.mt

Abstract

A simple two-dimensional linearized model of the atmosphere is used to investigate behavior of the geostrophic adjustment process on five selected horizontal hexagonal grids. This study shows that hexagonal lattices have some advantages over commonly used square grids. Having better isotropy, they provide more accurate dispersion of gravity waves than square grids do, and therefore they can be more appropriate for simulation of smaller-scale divergent processes. The gravity–inertia wave frequencies of most of the considered grids are also closer to the true solution than those on square grids. However, some hexagonal grids are not completely free of numerical inconsistencies. For example, one of the selected grids generates nonsymmetric roots of the gravity–inertia solution that may lead to the unwanted simulation of the atmospheric process. The analysis indicates which hexagonal distributions can be an appropriate choice for use in atmospheric and ocean models.

Corresponding author address: Slobodan Ničković, Euro-Mediterranean Centre on Insular Coastal Dynamics, Foundation for International Studies, University of Malta, St. Paul Street, Valletta, Malta. Email: nicko@icod.org.mt

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