On the stability and accuracy of the harmonic and biharmonic isoneutral mixing operators in ocean modelsстатья
Статья опубликована в высокорейтинговом журнале
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Дата последнего поиска статьи во внешних источниках: 29 сентября 2021 г.
Аннотация:Ocean models usually rely on a tracer mixing operator which diffuses along isoneutral directions. Thisrequirement is imposed by the highly adiabatic nature of the oceanic interior, and a numerical simulationneeds to respect these small levels of dianeutral mixing to maintain physically realistic results. For nonisopycnicmodels this is however non-trivial due to the non-alignment of the vertical coordinate isosurfaceswith local isoneutral directions, rotated mixing operators must therefore be used. This paper considersthe numerical solution of initial boundary value problems for the harmonic (Laplacian) andbiharmonic rotated diffusion operators. We provide stability criteria associated with the conventionalspace–time discretizations of the isoneutral Laplacian operator currently in use in general circulationmodels. Furthermore, we propose and study possible alternatives to those schemes. A new way to handlethe temporal discretization of the rotated biharmonic operator is also introduced. This scheme requiresonly the resolution of a simple one-dimensional tridiagonal system in the vertical direction to provide thesame stability limit of the non-rotated operator. The performance of the various schemes in terms of stabilityand accuracy is illustrated by idealized numerical experiments of the diffusion of a passive traceralong isoneutral directions.