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Modelling of Local Length-Scale Dynamics and Isotropizing Deformations: Formulation in Natural Coordinate System

In: Mathematical and Computational Approaches in Advancing Modern Science and Engineering

Author

Listed:
  • O. Pannekoucke

    (CERFACS/CNRS URA 1875
    CNRM/GAME, Météo-France/CNRS UMR 3589
    INPT-ENM)

  • E. Emili

    (CERFACS/CNRS URA 1875)

  • O. Thual

    (CERFACS/CNRS URA 1875
    Université de Toulouse; INPT, CNRS; IMFT)

Abstract

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.

Suggested Citation

  • O. Pannekoucke & E. Emili & O. Thual, 2016. "Modelling of Local Length-Scale Dynamics and Isotropizing Deformations: Formulation in Natural Coordinate System," Springer Books, in: Jacques Bélair & Ian A. Frigaard & Herb Kunze & Roman Makarov & Roderick Melnik & Raymond J. Spiteri (ed.), Mathematical and Computational Approaches in Advancing Modern Science and Engineering, pages 141-151, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-30379-6_14
    DOI: 10.1007/978-3-319-30379-6_14
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