Reference : Comparison of free-surface and rigid-lid finite element models of barotropic instabilities
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Earth sciences & physical geography
Comparison of free-surface and rigid-lid finite element models of barotropic instabilities
White, Laurent [Université catholique de Louvain - UCL >]
Beckers, Jean-Marie mailto [Université de Liège - ULiège > Département d'astrophys.]
Deleersnijder, Eric [Université catholique de Louvain - UCL >]
Legat, Vincent [Université catholique de Louvain - UCL >]
Ocean Dynamics
Springer Heidelberg
Yes (verified by ORBi)
[en] finite element method ; unstructured meshes ; barotropic instabilities ; free-surface flow
[en] 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.
Centre Interfacultaire de Recherches en Océanologie - MARE - GHER

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