Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory

We investigate three-dimensional quantum turbulence as described by the Gross-Pitaevskii model using analytical method exploited in Onsager "ideal turbulence" theory. derive scale-independence of scale-to-scale kinetic energy flux and establish a double-cascade scenario: at scales much larger than mean intervortex $\ell_i$, Richardson cascade becomes dominant, whereas smaller another type is induced stress. then evaluate corresponding velocity power spectrum phenomenological argument. The relation between novel cascade, which we call stress Kelvin-wave also discussed.