Regimes of turbulence without an energy cascade.

C F Barenghi,A W Baggaley,Y A Sergeev

doi:10.1038/srep35701

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.

Highlights

In analogy with classical turbulence, we are interested in the existence of a Richardson energy cascade in the hydrodynamic range kD k k, which is the regime of vortices interacting with each other; we are not interested in the k ≥ k regime of isolated vortex lines
Based on estimates for the effective dissipation rate in quantum turbulence considered at the hydrodynamic scales, that is in the range of scales corresponding to many vortices rather than individual vortex lines, we have obtained conditions necessary for existence of the kinetic energy cascade in the superfluid component and, of the k−5/3 scaling of the superfluid’s kinetic energy spectrum
The phenomenological approach which we have developed has enabled us to explain why, at finite temperatures, the Kolmogorov energy spectrum cannot be observed in 4He counterflows and 3He-B flows in the presence of stationary normal fluid

Summary

Objectives

Our aim is to develop a model which would yield conditions necessary for emergence of the quasiclassical quantum turbulence at very low temperatures such that the presemce of the normal fluid can be neglected. Note that our aim is to find conditions necessary for emergence of the quasiclassical regime which is associated with motion at scales larger than the intervortex distance

Methods

Results

Conclusion