Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory

Abstract

We refute the criticism expressed in a Comment by Krstulovic, L'vov, and Nazarenko [arXiv:2107.10598] on our paper [Phys. Rev. E 103, 023106 (2021)]. We first show that quantization of circulation is not ignored in our analysis. Then, we propose a more sophisticated analysis to avoid a subtle problem with the regularity of the velocity field. We thus defend the main results of our paper, which predicts the double-cascade scenario where the quantum stress cascade follows the Richardson cascade. We also provide a conjecture on the relation between the Kelvin-wave cascade and the quantum stress cascade.

Rotating quantum wave turbulence

“…Smaller values of ν are generally thought to originate from nearly parallel arrangement of vortices [20] and in the absence of vortex reconnections [43], both of which are realized in our experiments. We also note that while a recent theoretical work [26] put forward an idea of a 'quantum stress cascade' as a possible energy transfer mechanism, our observations -in particular the magnitude of the average vortex tilt θ determined mostly by KWs, the temperature dependence of the dissipative length scale k α , and the wave vector range of the excited KWs from k start to k end -imply the picture involving a cascade of KWs [24,25]. However, the outliers in the higher-temperature data in Figs.…”

“…To highlight differences between classical and quantum turbulence, the low-temperature limit is of particular interest since negligible frictional forces allow transfer of energy to length scales where quantization of vorticity is essential [19,23]. In this limit, the energy is believed to flow towards the smallest scales through a cascade of KWs [24,25] or through a quantum stress cascade [26] and is ultimately dissipated via emission of sound waves [27], emission of quasiparticles [28,29], or, at a finite temperature, via mutual friction [9,30]. Despite observations of vortex reconnections and the related production of KWs [31,32], direct experimental proof of the existence of the KW cascade has remained elusive.…”

Comment on "Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory''

“…In a recent paper, T. Tanogami presents a theoretical investigation of quantum turbulence at very low temperatures by adapting standard techniques used in classical hydrodynamics [1]. Following Onsager's ideas of classical turbulence [2], Tanogami proposes a double energy cascade scenario where the energy spectrum E v (k) behaves as…”

“…Here k is the wave vector, and C large and C small are positive constants. ℓ large is a scale that can be identified with the inertial scale of turbulence and ℓ small is defined using the quantum stress cospectrum (see [1]). Then, Tanogami defines the quantum baropycnal work flux Λ Σ ℓ and identifies the scale λ as the scale at which Λ Σ ℓ becomes constant.…”

“…Basically, Tanagomi's derivation completely ignores the quantization of velocity circulation, a crucial property of quantum turbulence that can not be neglected at scales smaller than ℓ i . We describe in the following our main criticisms on the double cascade scenario proposed in [1].…”