Zensho Yoshida (University of Tokyo)
The partition of enstrophy between zonal (ordered) and wavy (turbulent) components of vorticity has been studied for the beta-plane model of two-dimensional barotropic flow. A discrete set of zonal enstrophy levels is generated by the energy constraint; each level is specified by an eigenvalue that parallels the lamination period of zonal flow. The relaxation occurs by emitting small-scale wavy enstrophy, and continues as far as the nonlinear effect, scaled by the energy, can create wavy enstrophy. Comparison with numerical simulations shows that the theory gives a proper estimate of the zonal enstrophy in the relaxed state.