Toy model for vortex-ring-assisted particle drag in superfluid counterflow

Abstract

The interpretation of data obtained from particle image/tracking velocimetry in the study of superfluid flows has been so far a challenging task. Tracking particles (as solid hydrogen or deuterium) are attracted to the cores of quantized vortices, so that their dynamics can be strongly affected by the surrounding vortex tangle. Previous phenomenological arguments indicate that tracking particles and micro-sized vortex rings could form bound states (denoted here as VRP states). While a comprehensive description of the vortex ring-particle bonding mechanism has to deal with somewhat involved flow configurations, we introduce a simplified two-dimensional model of VRP states, which captures essential qualitative features of their three-dimensional counterparts. Besides an account of known experimental and numerical observations, the model proves to be of great heuristic interest. In particular, it sheds light on the important role played by viscous dissipation (due to the normal component of the fluid), the Magnus force, and topologically-excited vortex rings in the stability and dynamics of VRP states.

Hydrodynamic Decay of Decorated Quantum Vortex Rings

“…( 25) and ( 26) can be used to derive rough dimensional estimates of the several contributions in (22). The superfluid kinetic energy (23), for instance, would be estimated as…”

“…This approach has paved the way for an ongoing wave of new experiments, as the visualization of vortices near the superfluid transition [12], the study of quantum vortex reconnection [15], the decay of quantum vortex rings [16] -our main focus in this work -and the observation of Kelvin waves in vortex filaments [17]. Interesting open challenges are furthermore related to the amount of dynamic information that one can obtain from the recorded trajectories of tracking particles in superfluid turbulent regimes [18][19][20][21][22][23][24].…”