Abstract
We discuss the configurations of vortices in two-dimensional quantum turbulence, studying energy spectrum of superfluid velocity and correlation functions with the distance between two vortices. We apply the above method to quantum turbulence described by Gross-Pitaevskii equation in Bose-Einstein condensates. We make two-dimensional quantum turbulence from many dark solitons through the dynamical instability. A dark soliton is unstable and decays into vortices in two- and three-dimensional systems. In our work, we propose a method of discriminating between the uncorrelated turbulence and the correlated turbulence. We decompose the energy spectrum into two terms, namely the self-energy spectrum E self (k) made by individual vortices and the interactive energy spectrum E int (k) made by interference of two vortices. The uncorrelated turbulence is defined as turbulence with E int (k)≪E self (k), while the correlated turbulence is turbulence where E int (k) is not much smaller than E self (k). Our simulations show that in the decay of dark solitons, the vortices created consist of correlated pairs of opposite circulation vortices, leading to the correlated turbulence.
Highlights
Turbulence is one of the most challenging problems in fluid dynamics
As a method of making quantum turbulence (QT), this paper shows that 2D QT is created from many dark solitons through the dynamical instability [18, 19], which may occur in experiments when four BoseEinstein condensates (BECs) interfere
In order to determine whether 2D QT made by dark solitons is correlated or uncorrelated, we investigate the energy spectrum of the point vortex model and the correlation functions h±(l)
Summary
Turbulence is one of the most challenging problems in fluid dynamics. The circulation of vortices in classical turbulence (CT) has an arbitrary value and the core of a vortex is not well-defined due to the kinematic viscous diffusion. The turbulence decaying as L ∝ t−1 is called the random turbulence, which may be referred to as the uncorrelated turbulence These kinds of decay are related to the correlation between quantized vortices. In the semi-classical turbulence, turbulent energy is concentrated on scales l ∼ L−1/2 where l is the mean distance of vortices It exhibits a Kolmogorov spectrum, leading to the vortex line length decay L ∝ t−3/2. The total energy is mainly determined on the scale
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