Energy Spectra of Superfluid Turbulence in $^3$He

TL;DR

This paper investigates the energy spectra of superfluid turbulence in helium-3 using shell model simulations, revealing insights into its statistical properties and differences from classical turbulence.

Contribution

It introduces a shell model approach to study superfluid $^3$He turbulence and compares numerical results with analytical energy spectrum expressions.

Findings

Qualitative agreement between simulations and analytical spectra

Identification of energy distribution characteristics in superfluid turbulence

Insights into differences from classical turbulence regimes

Abstract

In superfluid $^3$He turbulence is carried predominantly by the superfluid component. To explore the statistical properties of this quantum turbulence and its differences from the classical counterpart we adopt the time-honored approach of shell models. Using this approach we provide numerical simulations of a Sabra-shell model that allows us to uncover the nature of the energy spectrum in the relevant hydrodynamic regimes. These results are in qualitative agreement with analytical expressions for the superfluid turbulent energy spectra that were found using a differential approximation for the energy flux.