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Sustained turbulence in the three-dimensional Gross–Pitaevskii model
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Proment, Davide, Nazarenko, Sergey and Onorato, Miguel (2012) Sustained turbulence in the three-dimensional Gross–Pitaevskii model. Physica D: Nonlinear Phenomena, Vol. 241 (No. 3). pp. 304-314. doi:10.1016/j.physd.2011.06.007 ISSN 01672789.
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Official URL: http://dx.doi.org/10.1016/j.physd.2011.06.007
Abstract
We study the three-dimensional forced–dissipated Gross–Pitaevskii equation. We force at relatively low wave numbers, expecting to observe a direct energy cascade and a consequent power-law spectrum of the form k−α. Our numerical results show that the exponent α strongly depends on how the inverse particle cascade is attenuated at ks lower than the forcing wave-number. If the inverse cascade is arrested by a friction at low ks, we observe an exponent which is in good agreement with the weak wave turbulence prediction k−1. For a hypo-viscosity, a k−2 spectrum is observed which we explain using a critical balance argument. In simulations without any low k dissipation, a condensate at k=0 is growing and the system goes through a strongly turbulent transition from a 4-wave to a 3-wave weak turbulence acoustic regime with evidence of k−3/2 Zakharov–Sagdeev spectrum. In this regime, we also observe a spectrum for the incompressible kinetic energy which formally resembles the Kolmogorov k−5/3, but whose correct explanation should be in terms of the Kelvin wave turbulence. The probability density functions for the velocities and the densities are also discussed.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Physica D: Nonlinear Phenomena | ||||
Publisher: | Elsevier BV | ||||
ISSN: | 01672789 | ||||
Official Date: | 2012 | ||||
Dates: |
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Volume: | Vol. 241 | ||||
Number: | No. 3 | ||||
Page Range: | pp. 304-314 | ||||
DOI: | 10.1016/j.physd.2011.06.007 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published |
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