| Abstract: |
| We revisit the derivation of the Lagrangian averaged Euler (LAE), or Euler-$\alpha$ 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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