Regimes of turbulence without an energy cascade

TL;DR

This paper investigates regimes of quantum turbulence in superfluid helium where the classical Kolmogorov energy cascade does not form, exploring physical mechanisms and conditions for quasiclassical behavior.

Contribution

It introduces simple physical models explaining the absence of Kolmogorov scaling and identifies conditions for quasiclassical turbulence in superfluid helium.

Findings

Physical mechanisms preventing Kolmogorov scaling in thermal counterflow.

Conditions for emergence of quasiclassical turbulence regimes.

Hydrodynamical models can describe unusual vortex dynamics.

Abstract

Experiments and numerical simulations of turbulent $^4$He and $^3$He-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.