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arXiv:2312.03968

Emergence of isotropy in rotating turbulence of Bose-Einstein condensates

Sano, Yuto, Makoto Tsubota

Published Dec 7, 2023• 0 citations
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Abstract

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 $k_z^{-2.5}$ in the direction parallel to the rotation axis. In contrast, the compressible kinetic energy exhibits an isotropic scaling behavior at high wavenumbers.

DOI
10.48550/arxiv.2312.03968

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We investigate the scaling of the energy cascade in a harmonically trapped, turbulent, rotating Bose-Einstein condensate in two dimensions. We achieve turbulence by injecting a localized perturbation into the condensate and gradually increasing its rotation frequency from an initial value to a maximum. The main characteristics of the resulting turbulent state depend on the initial conditions, rotation frequency, and ramp-up time. We analyze the energy and the fluxes of kinetic energy by considering initial profiles without vortices and with vortex lattices. In the case without initial vortices, we find the presence of Kolmogorov-like scaling (k−5/3) of the incompressible kinetic energy in the inertial range. However, with initial vortex lattices, the energy spectrum follows Vinen scaling (k−1) at transient iterations. For cases with high rotating frequencies, Kolmogorov-like scaling emerges at longer durations. We observe positive kinetic energy fluxes with both initial states across all final frequencies, indicating a forward cascade of incompressible and compressible kinetic energy.
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.
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Abstract The restoration of symmetries is one of the most fascinating properties of turbulence. We report a study of the emergence of isotropy in the Gross-Pitaevskii model with anisotropic forcing. Inspired by recent experiments, we study the dynamics of a Bose-Einstein condensate in a cylindrical box driven along the symmetry axis of the trap by a spatially uniform force. We introduce a measure of anisotropy A ( k , t ) defined on the momentum distributions , and study the evolution of A ( k , t ) and as turbulence proceeds. As the system reaches a steady state, the anisotropy, large at low momenta because of the large-scale forcing, is greatly reduced at high momenta. While exhibits a self-similar cascade front propagation, A ( k , t ) decreases without such self-similar dynamics. Finally, our numerical calculations show that the isotropy of the steady state is robust with respect to the amplitude of the drive.