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We performed numerical simulations of decaying quantum turbulence by using ageneralized Gross-Pitaevskii equation, that includes a beyond mean fieldcorrection and a nonlocal interaction potential. The nonlocal potential ischosen in order to mimic He II by introducing a roton minimum in the excitationspectrum. We observe that at large scales the statistical behavior of the flowis independent of the interaction potential, but at scales smaller than theintervortex distance a Kelvin wave cascade is enhanced in the generalizedmodel. In this range, the incompressible kinetic energy spectrum obeys the weakwave turbulence prediction for Kelvin wave cascade not only for the scalingwith wave numbers but also for the energy fluxes and the intervortex distance.

Kolmogorov and Kelvin wave cascades in a generalized model for quantum turbulence