Vortex shedding from a microsphere oscillating in superfluid ^4He at mK temperatures and from a laser beam moving in a Bose-Einstein condensate

TL;DR

This paper investigates vortex shedding and turbulence in superfluid helium and Bose-Einstein condensates, revealing linear relationships between vortex shedding frequency and velocity excess, and exploring the connection between superfluid Reynolds and Strouhal numbers.

Contribution

It demonstrates a linear dependence of vortex shedding frequency on velocity excess in superfluids and relates superfluid Reynolds and Strouhal numbers, extending turbulence understanding in quantum fluids.

Findings

Vortex shedding frequency scales linearly with velocity above critical velocity.

Number of vortices shed per half-period equals the superfluid Reynolds number.

A relation between superfluid Reynolds and Strouhal numbers is established.

Abstract

Turbulent drag of an oscillating microsphere, that is levitating in superfluid $^4$He at mK temperatures, is unstable slightly above a critical velocity amplitude $v_c$. The lifetime $\tau$ of the turbulent state is determined by the number $n$ of vortices shed per half-period. It is found that this number is identical to the superfluid Reynolds number. The possibility of moving a levitating sphere through superfluid $^3$He at microkelvin temperatures is considered. A laser beam moving through a Bose-Einstein condensate (BEC) (as observed by other authors) also produces vortices in the BEC. In particular, in either case a linear dependence of the shedding frequency $f_v$ on $\Delta v = v - v_c$ is observed, where $v$ is the velocity amplitude of the sphere or the constant velocity of the laser beam above $v_c$ for the onset of turbulent flow: $f_v = a \Delta v$, where the coefficient $a$ is proportional to the oscillation frequency $ \omega $ above some characteristic frequency $\omega_k$ and assumes a finite value for steady motion $\omega \rightarrow 0$. A relation between the superfluid Reynolds number and the superfluid Strouhal number is presented that is different from classical turbulence.