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Systematics of turbulence in the dissipationless, unforced, 2D, fourier-truncated Gross-Pitaevskii equation

Pandit, R and Shukla, V and Brachet, M (2020) Systematics of turbulence in the dissipationless, unforced, 2D, fourier-truncated Gross-Pitaevskii equation. In: 14th European Turbulence Conference, ETC 2013, 1-4 September 2013, Ecole Normale Superieure de LyonLyon, France.

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We carry out a systematic, direct numerical simulation (DNS) of the two-dimensional, Fourier-truncated, Gross-Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions. We find that the time evolution of this system can be classified into four regimes, which have qualitatively different statistical properties. In the first regime there are transients that depend on the initial conditions; in the second, power-law scaling regions, in the energy and the occupation-number spectra, appear and start to develop; the exponents of these power-laws and the extents of the scaling regions change with time and depended on the initial condition; in the third regime, the spectra drop rapidly for modes with wave numbers k > kc, and partial thermalization takes place for modes with k < kc; the self-truncation wave number kc(t) depends on the initial conditions and it grows either as a power of t or as log t; finally, in the fourth regime, complete thermalization is achieved and correlation functions and spectra are consistent with their nontrivial Berezinskii-Kosterlitz-Thouless forms, if we account for finite-size effect. Copyright © ETC 2013 - 14th European Turbulence Conference.All rights reserved.

Item Type: Conference Paper
Publication: ETC 2013 - 14th European Turbulence Conference
Publisher: Zakon Group LLC
Additional Information: The copyright of this article belongs to Zakon Group LLC.
Keywords: Bose-Einstein condensation, Correlation function; Finite size effect; Gross-Pitaevskii equation; Initial conditions; Kosterlitz-Thouless; Occupation numbers; Power law scalings; Statistical properties, Turbulence
Department/Centre: Division of Physical & Mathematical Sciences > Physics
Date Deposited: 03 Sep 2020 11:23
Last Modified: 08 Dec 2022 07:25
URI: https://eprints.iisc.ac.in/id/eprint/64895

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