# Vorticity and quantum turbulence in the merging of superfluid Helium nanodroplets

## TL;DR

This study investigates the dynamics of merging superfluid helium droplets, revealing vortex formation, turbulence regimes with Kolmogorov spectra, and roton radiation, providing insights into quantum turbulence phenomena.

## Contribution

It presents a detailed simulation of vortex nucleation and turbulence in merging superfluid helium droplets, linking microscopic vortex dynamics to macroscopic turbulent behavior.

## Key findings

- Vortex-antivortex rings nucleate and annihilate during merging.
- A Kolmogorov power law regime indicates quantum turbulence.
- Roton radiation dominates surface dynamics after vortex interactions.

## Abstract

We have studied the merging of two $^4$He droplets at zero temperature, caused by their Van der Waals mutual attraction. During the early stages of the merging, density structures appear which closely match the experimental observations by Vicente et al. [J. Low Temp. Phys. 121, 627 (2000)]. When the droplets are merging, quantized vortex-antivortex ring pairs nucleate at the surface and annihilate inside the merged droplet producing a roton burst. We also observe the nucleation of quantized vortex-antivortex rings that wrap the droplet surface and remain localized on the surface until they eventually decay into short-wavelength surface waves. Analysis of the kinetic energy spectrum discloses the existence of a regime where turbulence caused by vortex interaction and annihilation is characterized by a Kolmogorov power law. This is followed by another regime where roton radiation (produced by vortex-antivortex annihilation) dominates, whose hallmark is a weak, turbulent surface dynamics. We suggest that similar processes might appear in superfluid helium droplets after they capture impurities or if they are produced by hydrodynamic instability of a liquid jet. Experiments on collisions between recently-discovered self-bound Bose-Einstein condensates should display a similar phenomenology.