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Comparison of free-surface and rigid-lid finite element models of barotropic instabilities

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White, Laurent [UCL] Beckers, JM. Deleersnijder, Eric [UCL] Legat, Vincent [UCL]

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.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2006
Language Anglais
Journal information "Ocean Dynamics : theoretical, computational oceanography and monitoring" - Vol. 56, no. 2, p. 86-103 (2006)
Peer reviewed yes
Publisher Springer Heidelberg (Heidelberg)
issn 1616-7341
e-issn 1616-7228
Publication status Publié
Affiliation UCL - FSA/MECA - Département de mécanique
Keywords finite element method ; unstructured meshes ; barotropic instabilities ; free-surface flow
Links
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Bibliographic reference White, Laurent ; Beckers, JM. ; Deleersnijder, Eric ; Legat, Vincent. Comparison of free-surface and rigid-lid finite element models of barotropic instabilities. In: Ocean Dynamics : theoretical, computational oceanography and monitoring, Vol. 56, no. 2, p. 86-103 (2006)
Permanent URL http://hdl.handle.net/2078.1/38467