Generalized action invariants for drift waves-zonal flow systems

Generalized action invariants are identified for various models of drift waveturbulence in the presence of the mean shear flow. It is shown that the wavekinetic equation describing the interaction of the small scale turbulence andlarge scale shear flow can be naturally written in terms of these invariants.Unlike the wave energy, which is conserved as a sum of small- and large- scalecomponents, the generalized action invariant is shown to correspond to aquantity which is conserved for the small scale component alone. This invariantcan be used to construct canonical variables leading to a different definitionof the wave action (as compared to the case without shear flow). It issuggested that these new canonical action variables form a natural basis forthe description of the drift wave turbulence with a mean shear flow.Comment: 17 page