Regimes of turbulence without an energy cascade

Abstract

Experiments and numerical simulations of turbulent 4He and 3He-B have established that, at hydrodynamic length scales larger than the average distance between quantum vortices, the energy spectrum obeys the same 5/3 Kolmogorov law which is observed in the homogeneous isotropic turbulence of ordinary fluids. The importance of the 5/3 law is that it points to the existence of a Richardson energy cascade from large eddies to small eddies. However, there is also evidence of quantum turbulent regimes without Kolmogorov scaling. This raises the important questions of why, in such regimes, the Kolmogorov spectrum fails to form, what is the physical nature of turbulence without energy cascade, and whether hydrodynamical models can account for the unusual behaviour of turbulent superfluid helium. In this work we describe simple physical mechanisms which prevent the formation of Kolmogorov scaling in the thermal counterflow, and analyze the conditions necessary for emergence of quasiclassical regime in quantum turbulence generated by injection of vortex rings at low temperatures. Our models justify the hydrodynamical description of quantum turbulence and shed light into an unexpected regime of vortex dynamics.

Inviscid diffusion of vorticity in low-temperature superfluid helium

“…Usually the answer is given in terms of the energy spectrum, but in this case the turbulence is neither steady nor homogeneous, and the interpretation of the spectrum would be difficult. We proceed differently and calculate the transverse velocity correlation function 2 , and find that it rapidly decreases with distance, meaning that the turbulent velocity field is essentially random; at t = 0, we find that f ⊥ (ℓ/2, 0) ≈ 0.27 only, where ℓ is the intervortex spacing, indicative of the Vinen (ultra-quantum) regime of quantum turbulence [5], characterized by the absence of an energy cascade [4]. Similar turbulence and correlation functions have been predicted in trapped atomic Bose-Einstein condensates [27].…”

“…Most experimental, theoretical and numerical studies have addressed quantum turbulence in its simplest form: statistically-steady, homogeneous and isotropic. These studies have revealed similarities and differences with respect to ordinary turbulence, in terms of energy spectra [2][3][4], decay [5,6], intermittency [7][8][9] and velocity statistics [10][11][12]. Much less is known about turbulence which is inhomogeneous, in particular turbulence which is initially confined in a small region of space and is free to spread out.…”

Numerical Studies of Quantum Turbulence

“…At these short length scales, the quantum nature of the vorticity is dominant, and the energy should be transferred by cascade along Kelvin waves (Kelvin-wave cascade) until some short wavelength where dissipation due to phonon emission is expected to be effective. It is important to know the condition that which of the two types of turbulence appears actually; the mechanism of preventing the formation of the quasiclassical Kolmogorov spectrum is recently discussed [46]. A simulation of the VF model in a three-dimensional (3D) periodic box confirms the Kolmogorov −5/3 spectrum [47,48].…”

Vinen turbulence via the decay of multicharged vortices in trapped atomic Bose-Einstein condensates

“…This finding suggests that turbulence of quantized vortices (quantum turbulence) may represent the 'skeleton' of ordinary (classical) turbulence [3]. A puzzle arises however: experiments [4,5] show that there are other regimes in which turbulent superfluid helium lacks the Kolmogorov spectrum.…”