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

We performed numerical simulations of decaying quantum turbulence by using a generalized Gross-Pitaevskii equation that includes a beyond mean field correction and a nonlocal interaction potential. The nonlocal potential is chosen in order to mimic He II by introducing a roton minimum in the excitation spectrum. We observe that at large scales the statistical behavior of the flow is independent of the interaction potential, but at scales smaller than the intervortex distance a Kelvin wave cascade is enhanced in the generalized model. In this range, the incompressible kinetic energy spectrum obeys the weak wave turbulence prediction for Kelvin wave cascade not only for the scaling with wave numbers but also for the energy flux and the intervortex distance.