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Lagrangian averaging with geodesic mean

Marcel Oliver
Published 15 November 2017.DOI: 10.1098/rspa.2017.0558
Marcel Oliver
School of Engineering and Science, Jacobs University, 28759 Bremen, Germany
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Abstract

This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler-α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.

  • Received August 11, 2017.
  • Accepted September 28, 2017.
  • © 2017 The Author(s)
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November 2017
Volume 473
, issue 2207
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science: 473 (2207)
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Keywords

Euler equations
Lagrangian averaging
generalized Lagrangian mean
Taylor hypothesis
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Lagrangian averaging with geodesic mean
Marcel Oliver
Proc. R. Soc. A 2017 473 20170558; DOI: 10.1098/rspa.2017.0558. Published 15 November 2017
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Lagrangian averaging with geodesic mean

Marcel Oliver
Proc. R. Soc. A 2017 473 20170558; DOI: 10.1098/rspa.2017.0558. Published 15 November 2017

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  • Article
    • Abstract
    • 1. Introduction
    • 2. Lagrangian averaging
    • 3. The Marsden–Shkoller–Taylor hypotheses
    • 4. Geodesic mean
    • 5. Lagrangian averaging as a geodesic generalized Lagrangian mean closure
    • 6. Discussion
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    • Competing interests
    • Funding
    • Acknowledgements
    • References
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  • mathematical modelling
  • fluid mechanics
  • applied mathematics

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