Identifying a superfluid Reynolds number via dynamical similarity

TL;DR

This paper introduces a superfluid Reynolds number, ${ m Re}_s$, to characterize vortex shedding and turbulence transition in superfluid flows, revealing universal behavior similar to classical fluids.

Contribution

The study defines a superfluid Reynolds number based on vortex shedding frequencies, establishing a universal criterion for turbulence onset in superfluid flows.

Findings

Vortex shedding frequency scales with ${ m Re}_s$ in superfluids.

Transition to turbulence occurs at ${ m Re}_s oughly 0.7$.

Universal behavior matches classical empirical relations.

Abstract

The Reynolds number provides a characterization of the transition to turbulent flow, with wide application in classical fluid dynamics. Identifying such a parameter in superfluid systems is challenging due to their fundamentally inviscid nature. Performing a systematic study of superfluid cylinder wakes in two dimensions, we observe dynamical similarity of the frequency of vortex shedding by a cylindrical obstacle. The universality of the turbulent wake dynamics is revealed by expressing shedding frequencies in terms of an appropriately defined superfluid Reynolds number, ${\rm Re}_s$, that accounts for the breakdown of superfluid flow through quantum vortex shedding. For large obstacles, the dimensionless shedding frequency exhibits a universal form that is well-fitted by a classical empirical relation. In this regime the transition to turbulence occurs at ${\rm Re}_s\approx 0.7$, irrespective of obstacle width.