Comparison of free-surface and rigid-lid finite element models of barotropic instabilities |
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Authors: | Laurent White Jean-Marie Beckers Eric Deleersnijder Vincent Legat |
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Institution: | (1) Centre for Systems Engineering and Applied Mechanics (CESAME), Université catholique de Louvain, 4, Avenue G. Lemaître, 1348 Louvain-la-Neuve, Belgium;(2) G. Lemaître Institute of Astronomy and Geophysics (ASTR), Université catholique de Louvain, 2, Chemin du Cyclotron, 1348 Louvain-la-Neuve, Belgium;(3) Geohydrodynamics and Environmental Research, Université de Liège,, Sart Tilman B-5, 4000 Liège, Belgium |
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Abstract: | The main goal of this work is to appraise the finite element method in the way it represents barotropic instabilities. To that end, three different formulations are employed. The free-surface formulation solves the primitive shallow-water equations and is of predominant use for ocean modeling. The vorticity–stream function and velocity–pressure formulations resort to the rigid-lid approximation and are presented because theoretical results are based on the same approximation. The growth rates for all three formulations are compared for hyperbolic tangent and piecewise linear shear flows. Structured and unstructured meshes are utilized. The investigation is also extended to time scales that allow for instability meanders to unfold, permitting the formation of eddies. We find that all three finite element formulations accurately represent barotropic instablities. In particular, convergence of growth rates toward theoretical ones is observed in all cases. It is also shown that the use of unstructured meshes allows for decreasing the computational cost while achieving greater accuracy. Overall, we find that the finite element method for free-surface models is effective at representing barotropic instabilities when it is combined with an appropriate advection scheme and, most importantly, adapted meshes. |
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Keywords: | Finite element method Unstructured meshes Barotropic instabilities Free-surface flow |
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