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

Abstract

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.

Vortex clustering, polarisation and circulation intermittency in classical and quantum turbulence

“…First, we see that the turbulent case displays a clear k −5/3 range, in agreement with the energy spectra obtained from the full GP and NS fields. Note that, in the case of GP fields, we show the incompressible kinetic energy spectrum, which contains 86% of the total energy of the system—the other components being the compressible, internal and quantum energy 20 , 22 . Secondly, the K41 scaling disappears once polarisation is artificially suppressed from the tangle, leading to a trivial k −1 scaling range for the disordered state (see “Methods” for a brief derivation).…”

“…Details on the chosen parameters can be found in Ref. 22 . The use of a standard or a generalised GP model does not affect the statistics of velocity circulation 13 .…”

“…The generalised GP equation ( 9 ) is solved in a three-dimensional periodic cube by direct numerical simulations using the Fourier pseudospectral code FROST, with an explicit fourth-order Runge–Kutta method for the time integration 22 . The quantum turbulent regime is studied in a freely decaying Arnold–Beltrami–Childress (ABC) flow 13 , 21 with 2048 3 collocation points.…”

“…Indeed, at such scales, a Kolmogorov turbulent cascade is observed, provided that a large-scale separation exists between ℓ and the largest scale of the system. In particular, the scaling law predicted by Kolmogorov's celebrated K41 theory 17 for the kinetic energy spectrum has been observed in superfluid helium experiments 18,19 and in numerical simulations of quantum turbulence [20][21][22] .…”

Critical velocity for vortex nucleation and roton emission in a generalized model for superfluids

“…The study of vortices in superfluid 4 He presents some difficulties given that there is not a simple microscopic description of it. However, it is possible to study some of its phenomenology assuming a non-local interaction between the bosons constituting the superfluid [26][27][28][29]. In this framework, a moving obstacle is allowed to emit some density excitations known as rotons [29][30][31].…”