Local shell-to-shell energy transfer via nonlocal interactions in fluid turbulence

In this paper we analytically compute the strength of nonlinear interactions in a triad, and the energy exchanges between wave-number shells in incompressible fluid turbulence. The computation has been done using first-order perturbative field theory. In three dimensions, magnitude of triad interact...

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Bibliographic Details
Published in:Pramāṇa 2005-08, Vol.65 (2), p.297-310, Article 297
Main Authors: Verma, Mahendra K, Ayyer, Arvind, Debliquy, Olivier, Kumar, Shishir, Chandra, Amar V
Format: Article
Language:English
Subjects:
Energy
Energy transfer
Field theory
Fluid dynamics
Fluid flow
Incompressible flow
Incompressible fluids
Three dimensional analysis
Turbulence
Turbulent flow
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Summary:In this paper we analytically compute the strength of nonlinear interactions in a triad, and the energy exchanges between wave-number shells in incompressible fluid turbulence. The computation has been done using first-order perturbative field theory. In three dimensions, magnitude of triad interactions is large for nonlocal triads, and small for local triads. However, the shell-to-shell energy transfer rate is found to be local and forward. This result is due to the fact that the nonlocal triads occupy much less Fourier space volume than the local ones. The analytical results on three-dimensional shell-to-shell energy transfer match with their numerical counterparts. In two-dimensional turbulence, the energy transfer rates to the nearby shells are forward, but to the distant shells are backward; the cumulative effect is an inverse cascade of energy.
ISSN:0304-4289
0973-7111
DOI:10.1007/BF02898618