Homogeneous Isotropic Superfluid Turbulence in Two Dimensions: Inverse and Forward Cascades in the Hall-Vinen-Bekharevich-Khalatnikov model

TL;DR

This study uses direct numerical simulations to analyze two-dimensional superfluid turbulence, revealing dual cascade behaviors and velocity alignments, providing insights and experimental suggestions for superfluid turbulence.

Contribution

First direct numerical simulation study of 2D superfluid turbulence in the Hall-Vinen-Bekharevich-Khalatnikov model, identifying inverse and forward cascades and velocity alignment.

Findings

Normal-fluid and superfluid energy spectra show two power-law regimes.

Evidence of inverse energy cascade and forward enstrophy cascade.

Quantified mutual friction effects on velocity alignment.

Abstract

We present the first direct-numerical-simulation study of the statistical properties of two-dimensional superfluid turbulence in the Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both normal-fluid and superfluid energy spectra can exhibit two power-law regimes, the first associated with an inverse cascade of energy and the second with the forward cascade of enstrophy. We quantify the mutual-friction-induced alignment of normal and superfluid velocities by obtaining probability distribution functions of the angle between them and the ratio of their moduli. Our study leads to specific suggestions for experiments.