Journal
PHYSICAL REVIEW A
Volume 99, Issue 4, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevA.99.043605
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Funding
- ECOS-Sud Grant [A13E01]
- European Research Council under the European Community's Seventh Framework Program, ERC [339032]
- Grant PICT [2015-3530]
- Agence Nationale de la Recherche [GIANTE ANR-18-CE30-0020-01]
- [IDRIS 100591]
- [DARI x20152a7493]
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We study freely decaying quantum turbulence by performing high-resolution numerical simulations of the Gross-Pitaevskii equation (GPE) in the Taylor-Green geometry. We use resolutions ranging from 1024(3) to 4096(3) grid points. The energy spectrum confirms the presence of both a Kolmogorov scaling range for scales larger than the intervortex scale l, and a second inertial range for scales smaller than l. Vortex line visualizations show the existence of substructures formed by a myriad of small-scale knotted vortices. Next, we study finite-temperature effects in decaying quantum turbulence by using the stochastic Ginzburg-Landau equation to generate thermal states, and then by evolving a combination of these thermal states with the Taylor-Green initial conditions under the GPE. We use finite-temperature GPE simulations to extract mean-free path by measuring the spectral broadening in the Bogoliubov dispersion relation that we obtain from the spatiotemporal spectra, and use it to quantify the effective viscosity as a function of the temperature. Finally, we perform low-Reynolds-number simulations of the Navier-Stokes equations, in order to compare the decay of high-temperature quantum flows with their classical counterparts, and to further calibrate the estimations of the effective viscosity (based on the mean-free-path computations).
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