Generalized vorticity in transitional quantum turbulence

TL;DR

This paper investigates the transition to Bose-Einstein condensation in a bosonic gas using the Gross-Pitaevskii equation, highlighting the role of generalized vorticity and enstrophy invariance in transitional turbulence, supported by numerical simulations.

Contribution

It introduces a generalized vorticity framework and demonstrates how enstrophy invariance governs transitional turbulence before condensate formation, supported by 3D numerical simulations.

Findings

Enstrophy based on generalized vorticity controls turbulence dynamics.

Occupation number spectrum scales as N_k ~ k^{-1} during transition.

Numerical simulations support the theoretical model.

Abstract

Transition to condensate state in the degenerate gas of bosons is studied using the Gross-Pitaevskii equation. It is shown that adiabatic invariance of an enstrophy (mean squared vorticity) based on a generalized vorticity $curl (|\psi|^2 {\bf v})/|\psi|^2$, controls dynamics of the transitional turbulence just before formation of the condensate with its tangles of quantized vortices ($|\psi|^2 {\bf v}$ is the weighted velocity field defined on the macroscopic wave function $\psi$). Scaling of the angle-averaged occupation number spectrum, $N_k \sim k^{-1}$, has been obtained for the free developing transitional turbulence for the weak nonlinear (and completely disordered) initial conditions. Results of the three-dimensional numerical simulations have been used to support the theoretical consideration.