The Euler-Poincar\'e approach to complex fluids is used to derive multiscale
equations for computationally modelling Euler flows as a basis for modelling
turbulence. The model is based on a \emph{kinematic sweeping ansatz} (KSA)
which assumes that the mean fluid flow serves as a Lagrangian frame of motion
for the fluctuation dynamics. Thus, we regard the motion of a fluid parcel on
the computationally resolvable length scales as a moving Lagrange coordinate
for the fluctuating (zero-mean) motion of fluid parcels at the unresolved
scales. Even in the simplest 2-scale version on which we concentrate here, the
contributions of the fluctuating motion under the KSA to the mean motion yields
a system of equations that extends known results and appears to be suitable for
modelling nonlinear backscatter (energy transfer from smaller to larger scales)
in turbulence using multiscale methods.Comment: 1st version, comments welcome! 23 pages, no figures. In honor of
Peter Constantin's 60th birthda
