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M. Oliver,
Lagrangian averaging with geodesic mean,
Proc. R. Soc. Lond. A 473 (2017), 20170558.
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 an Euclidean spatial domain
without boundaries.
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