Scaling laws of wave-cascading superfluid turbulence

Y Narita

doi:10.1063/1.4985725

Abstract

Phenomenological model is constructed for superfluid turbulence for two distinct energy cascade scenarios, sound wave cascade and critically-balanced Kelvin wave cascade, using the method for magneto-fluid turbulence theory. Excitations along dispersion relations are used as the primary energy reservoir. The spectral indices in the inertial range are estimated as −3/2 for the long-wavelength sound wave cascade, −3 in the direction to the mean filaments for the Kelvin wave cascade, and −5/3 perpendicular to the filament direction.

Highlights

In the modern physics context, turbulence is regarded as a restoration of the scaling symmetry intrinsic to the governing equation (e.g., Navier-Stokes equation in the high Reynolds number limit).[1]
Superfluid turbulence is a fascinating phenomenon in that (1) turbulence occurs in a collisionless medium and (2) there are a higher degree of freedom in the energy cascade mechanisms in the inertial range, including linear mode wave interactions, vortex filament entanglement, and vortex reconnections
Nucleons are believed to be a superfluid state in the neutron star crust and core

Summary

INTRODUCTION

In the modern physics context, turbulence is regarded as a restoration of the scaling symmetry intrinsic to the governing equation (e.g., Navier-Stokes equation in the high Reynolds number limit).[1]. The transition from the hydrodynamic-like cascade into the Kelvin wave cascade may be smooth and keep the same spectral slope of 5/3.37 Sound waves are produced, for example, by quantum vortex reconnection,[38,39] and can potentially develop into wave turbulence as the sound waves can interact with themselves.[8] The formation of multiple inertial range is proposed to model the superfluid turbulence energy spectrum.[40]. The goal of this manuscript is to contribute to the understanding of the scaling laws for superfluid wave turbulence. For the Kelvin wave cascade (incompressible turbulence) the index is 3 in the parallel direction (to the local filament) and 5/3 in the perpendicular direction

Theoretical building blocks

Sound wave turbulence

Kelvin wave turbulence

OUTLOOK