Lagrangian reduction and wave mean flow interaction

How does one derive models of dynamical feedback effects in multiscale, multiphysics systems such as wave mean flow interaction (WMFI)? We shall address this question for hybrid systems, defined whose motion can be expressed the composition two or more Lie-group actions. Hybrid abound fluid dynamics. Examples include: dynamics complex fluids liquid crystals; wind-driven waves propagating with currents moving on sea surface; turbulence modelling and plasmas; classical-quantum hydrodynamic molecular chemistry. From among these examples, motivating here is: do produce ocean surface currents? The paper first summarises geometric mechanics approach deriving motions ideal It then illustrates WMFI examples 3D WKB 2D amplitudes governed by nonlinear Schrödinger (NLS) equation frame an incompressible inhomogeneous Euler flow. results tell us that not create waves, although it transport waves. However, opposite direction is possible, since NLS discussed fact circulatory