Evolution of a superfluid vortex filament tangle driven by the Gross-Pitaevskii equation

Comment on "Theoretical analysis of quantum turbulence using the Onsager ideal turbulence theory"

In a recent paper, Tanogami [Phys. Rev. E 103, 023106 (2021)2470-004510.1103/PhysRevE.103.023106] proposes a scenario for quantum turbulence where the energy spectrum at scales smaller than the intervortex distance is dominated by a quantum stress cascade, in opposition to Kelvin-wave cascade predictions. The purpose of the present Comment is to highlight some physical issues in the derivation of the quantum stress cascade, in particular to stress that quantization of circulation has been ignored.

Irreversible Dynamics of Vortex Reconnections in Quantum Fluids

We statistically study vortex reconnections in quantum fluids by evolving different realizations of vortex Hopf links using the Gross-Pitaevskii model. Despite the time reversibility of the model, we report clear evidence that the dynamics of the reconnection process is time irreversible, as reconnecting vortices tend to separate faster than they approach. Thanks to a matching theory devised concurrently by Proment and Krstulovic [Phys. Rev. Fluids 5, 104701 (2020)PLFHBR2469-990X10.1103/PhysRevFluids.5.104701], we quantitatively relate the origin of this asymmetry to the generation of a sound pulse after the reconnection event. Our results have the prospect of being tested in several quantum fluid experiments and, theoretically, may shed new light on the energy transfer mechanisms in both classical and quantum turbulent fluids.

Momentum of vortex tangles by weighted area information

Here we show how to apply a recently introduced method based on the geometric interpretation of linear momentum of vortex lines to determine dynamical properties of a network of knots and links. To show how the method works and to prove its feasibility, we consider the evolution of quantum vortices governed by the Gross-Pitaevskii equation. Accurate estimates of the momentum of interacting and reconnecting vortex rings, links, and knots are determined. The method is of general validity and it proves particularly useful in practical situations where no analytical information is available. It can be easily adapted to situations where morphological information can be extracted from experimental or computational data, thus providing a powerful tool for real-time diagnostics of vortex filaments or other networks of filamentary structures.

Vortex knots on three-dimensional lattices of nonlinear oscillators coupled by space-varying links

Quantized vortices in a complex wave field described by a defocusing nonlinear Schrödinger equation with a space-varying dispersion coefficient are studied theoretically and compared to vortices in the Gross-Pitaevskii model with external potential. A discrete variant of the equation is used to demonstrate numerically that vortex knots in three-dimensional arrays of oscillators coupled by specially tuned weak links can exist for as long times as many as tens of typical vortex turnover periods.

Quantum Ferrofluid Turbulence

We study the elementary characteristics of turbulence in a quantum ferrofluid through the context of a dipolar Bose gas condensing from a highly nonequilibrium thermal state. Our simulations reveal that the dipolar interactions drive the emergence of polarized turbulence and density corrugations. The superfluid vortex lines and density fluctuations adopt a columnar or stratified configuration, depending on the sign of the dipolar interactions, with the vortices tending to form in the low-density regions to minimize kinetic energy. When the interactions are dominantly dipolar, the decay of the vortex line length is enhanced, closely following a t^{-3/2} behavior. This system poses exciting prospects for realizing stratified quantum turbulence and new levels of generating and controlling turbulence using magnetic fields.