Scale invariance and superfluid turbulence

TL;DR

This paper develops a scale-invariant Schrödinger field theory that models superfluid turbulence, analytically deriving the Kolmogorov 5/3 law and revealing a Biot-Savart interaction among filament excitations.

Contribution

It introduces a novel scale-invariant Schrödinger field theory that effectively describes superfluid turbulence and its key statistical and interaction properties.

Findings

Derivation of the Kolmogorov 5/3 law from the theory

Identification of a Biot-Savart interaction among filament excitations

Establishment of the theory as an effective model for superfluid turbulence

Abstract

We construct a Schroedinger field theory invariant under local spatial scaling. It is shown to provide an effective theory of superfluid turbulence by deriving, analytically, the observed Kolmogorov 5/3 law and to lead to a Biot-Savart interaction between the observed filament excitations of the system as well.