Local shell-to-shell energy transfer via nonlocal interactions in fluid turbulence |
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Authors: | Mahendra K Verma Arvind Ayyer Olivier Debliquy Shishir Kumar Amar V Chandra |
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Institution: | (1) Department of Physics, Indian Institute of Technology, 208 016 Kanpur, India;(2) Department of Physics and Astronomy, Rutgers University, Piscataway, NJ, USA;(3) Statistical and Plasma Physics, Université Libre de Bruxelles, CP231, Campus Plaine, 1050 Brussels, Belgium;(4) Centre for High Energy Physics, Indian Institute of Science, 560 012 Bangalore, India |
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Abstract: | 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. |
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Keywords: | Homogeneous and isotropic turbulence local transfer |
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