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. ISSN 01672789

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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
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Physica D: Nonlinear Phenomena
Publisher:	Elsevier BV
ISSN:	01672789
Official Date:	2012
Volume:	Vol. 241
Number:	No. 3
Page Range:	pp. 304-314
Identification Number:	10.1016/j.physd.2011.06.007
Status:	Peer Reviewed
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/43617

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