Statistics of Lagrangian quantum turbulence

TL;DR

This paper develops an analytical superstatistical Langevin model to describe the velocity distribution of tracer particles in turbulent quantum liquids, accurately matching experimental and simulation data.

Contribution

It introduces a novel superstatistical Langevin framework for quantum turbulence, providing an analytical PDF that captures observed velocity distributions.

Findings

Derived an analytical velocity PDF with correct tails and center behavior.

The model matches experimental and numerical data with high accuracy.

Results are universal, independent of specific quantum fluid details.

Abstract

We consider the dynamics of small tracer particles in turbulent quantum liquids. The complicated interaction processes of vortex filaments, the quantum constraints on vorticity and the varying influence of both the superfluid and the normal fluid on the tracer particle effectively lead to a superstatistical Langevin-like model that in a certain approximation can be solved analytically. An analytic expression for the PDF of velocity v of the tracer particle is derived that exhibits not only the experimentally observed $v^-3$ tails but also the correct behavior near the center of the distribution, in excellent agreement with experimental measurements and numerical simulations. Our results are universal and do not depend on details of the quantum fluid.