Modelling of Local Length-Scale Dynamics and Isotropizing Deformations
Résumé
We propose an algorithm to model anisotropic correlation functions using an approach based on the deformation of locally isotropic ones. In a previous work, a set of equations that allow to calculate the desired deformation was derived for a flat coordinates system. However this strategy is not adapted for curved geometry as the sphere (regional and global atmospheric models), where it is suitable to state the local isotropy in terms of the local Riemannian metric.This paper introduces the theoretical background to deal explicitly with natural coordinate systems leading to a formulation adapted with the Riemannian metric. It results that the isotropizing deformation is obtained from the resolution of coupled non-linear equations depending on the geometry. This procedure is illustrated within a 2D setting.
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