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International Conference on Low Temperature Physics (LT)

Anisotropic Energy Spectrum in Decaying Rotating Turbulence in the Gross–Pitaevskii Model

Yuto Sano, Makoto Tsubota

Published May 22, 2023• 0 citations
Publisher

Abstract

We investigate the dynamics of a decaying rotating turbulence using the dissipative Gross-Pitaevskii model.The turbulence is created by oscillating a Bose-Einstein condensate trapped in a cylindrical box potential.After the turbulence appears with the energy spectrum of a power law, we turn off the oscillation and rotate the condensate with an angular frequency Ω, thus realizing a decaying rotating turbulence.When Ω is low, the condensate shows a turbulent structure, and the power law behavior is modified by the rotation.For higher Ω, quantized vortices along the rotation axis are created.For much higher Ω, the stronger centrifugal force creates a 'giant vortex' that includes phase singularities in the central low-density hole, which yields an anisotropic energy spectrum.

DOI
10.7566/jpscp.38.011015

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We investigate the dynamics of a decaying rotating turbulence using the dissipative Gross-Pitaevskii model.The turbulence is created by oscillating a Bose-Einstein condensate trapped in a cylindrical box potential.After the turbulence appears with the energy spectrum of a power law, we turn off the oscillation and rotate the condensate with an angular frequency Ω, thus realizing a decaying rotating turbulence.When Ω is low, the condensate shows a turbulent structure, and the power law behavior is modified by the rotation.For higher Ω, quantized vortices along the rotation axis are created.For much higher Ω, the stronger centrifugal force creates a 'giant vortex' that includes phase singularities in the central low-density hole, which yields an anisotropic energy spectrum.
We present a study on the development of rotating turbulence in Bose-Einstein condensates with a dissipative Gross-Pitaevskii model. Turbulence is generated by driving the lattice of quantized vortices in a harmonic potential with a random forcing potential. As the turbulence progressed, the initial alignment of vortices underwent slight disruptions, thereby increasing the high-wavenumber components of the kinetic energy. In the turbulent state, the distribution of incompressible kinetic energy exhibits milder anisotropy than that in the initial lattice state and demonstrates a scaling behavior of kz−2.5k_z^{-2.5}kz−2.5​ in the direction parallel to the rotation axis. In contrast, the compressible kinetic energy exhibits an isotropic scaling behavior at high wavenumbers.
We show the generation of two-dimensional quantum turbulence through simulations of a giant vortex decay in a trapped Bose-Einstein condensate. While evaluating the incompressible kinetic energy spectra of the quantum fluid described by the Gross-Pitaevskii equation, a bilinear form in a log-log plot is verified. A characteristic scaling behavior for small momenta shows resemblance to the Kolmogorov k−5/3k^{-5/3}k−5/3 law, while for large momenta it reassures the universal behavior of the core-size k−3k^{-3}k−3 power-law. This indicates a mechanism of energy transportation consistent with an inverse cascade. The feasibility of the described physical system with the currently available experimental techniques to create giant vortices opens up a new route to explore quantum turbulence.
We investigate two-dimensional turbulence in finite-temperature trapped Bose-Einstein condensates within damped Gross-Pitaevskii theory. Turbulence is produced via circular motion of a Gaussian potential barrier stirring the condensate. We systematically explore a range of stirring parameters and identify three regimes, characterized by the injection of distinct quantum vortex structures into the condensate: (A) periodic vortex dipole injection, (B) irregular injection of a mixture of vortex dipoles and co-rotating vortex clusters, and (C) continuous injection of oblique solitons that decay into vortex dipoles. Spectral analysis of the kinetic energy associated with vortices reveals that regime (B) can intermittently exhibit a Kolmogorov ${k}^{\ensuremath{-}5/3}$ power law over almost a decade of length or wave-number (kkk) scales. The kinetic energy spectrum of regime (C) exhibits a clear ${k}^{\ensuremath{-}3/2}$ power law associated with an inertial range for weak-wave turbulence and a ${k}^{\ensuremath{-}7/2}$ power law for high wave numbers. We thus identify distinct regimes of forcing for generating either two-dimensional quantum turbulence or classical weak-wave turbulence that may be realizable experimentally.
We study two-dimensional quantum turbulence in miscible binary Bose-Einstein condensates in either a harmonic trap or a steep-wall trap through the numerical simulations of the Gross-Pitaevskii equations. The turbulence is generated through a Gaussian stirring potential. When the condensates have unequal intracomponent coupling strengths or asymmetric trap frequencies, the turbulent condensates undergo a dramatic decay dynamics to an interlaced array of vortex-antidark structures, a quasiequilibrium state, of like-signed vortices with an extended size of the vortex core. The time of formation of this state is shortened when the parameter asymmetry of the intracomponent couplings or the trap frequencies is enhanced. The corresponding spectrum of the incompressible kinetic energy exhibits two noteworthy features: (i) a ${k}^{\ensuremath{-}3}$ power law around the range of the wave number determined by the spin healing length (the size of the extended vortex core) and (ii) a flat region around the range of the wave number determined by the density healing length. The latter is associated with the small scale phase fluctuation relegated outside the Thomas-Fermi radius and is more prominent as the strength of intercomponent interaction approaches the strength of intracomponent interaction. We also study the impact of the intercomponent interaction to the cluster formation of like-signed vortices in an elliptical steep-wall trap, finding that the intercomponent coupling gives rise to the decay of the clustered configuration.
We numerically model turbulence in a trapped atomic Bose-Einstein condensate by solving the Gross-Pitaevskii nonlinear Schroedinger equation. We find that, after an initial growth, the vortex length decays approximately as t(-1) where t is time, consistent with experiments in turbulent superfluid helium, and that the velocity components obey power-law statistics, again in agreement with observations in turbulent superfluid helium. We find the same statistics, which contrasts to the Gaussian statistics observed in ordinary classical turbulence, in a variety of quantum fluids in two and three dimensions (trapped condensates, homogeneous condensates, vortex points, vortex filaments). We argue that the non-Gaussianity arises from the singular nature of quantised vorticity.