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

摘要

In this paper we analytically compute the strength of nonlinear interactionsin a triad, and the energy exchanges between wavenumber shells inincompressible fluid turbulence. The computation has been done usingfirst-order perturbative field theory. In three dimension, magnitude of triadinteractions 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. Thisresult is due to the fact that the nonlocal triads occupy much less Fourierspace volume than the local ones. The analytical results on three-dimensionalshell-to-shell energy transfer match with their numerical counterparts. Intwo-dimensional turbulence, the energy transfer rates to the near-by shells areforward, but to the distant shells are backward; the cumulative effect is aninverse cascade of energy.