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

Details Local shell-to-shell energy transfer via nonlocal Interactions in fluid turbulence Local shell-to-shell energy transfer via nonlocal Interactions in fluid turbulence

2002-04-14

arxiv.org/abs/nlin/0204027v4

Pramana, v65, 297, 2005

Nonlinear Sciences

Chaotic Dynamics

10 pages, Revtex4

Scientific paper

10.1007/BF02898618

In this paper we analytically compute the strength of nonlinear interactions in a triad, and the energy exchanges between wavenumber shells in incompressible fluid turbulence. The computation has been done using first-order perturbative field theory. In three dimension, 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 near-by shells are forward, but to the distant shells are backward; the cumulative effect is an inverse cascade of energy.

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