On the localness of the spectral energy transfer in turbulence

Abstract

By utilizing available experimental data for net energy transfer spectra for homogeneous turbulence, contributions P(κ, κ′) to the energy transfer at a wavenumber κ from various other wavenumbers κ′ are calculated. This is done by fitting a truncated power-exponential series in κ and κ′ to the experimental data for the net energy transfer T(κ), and using known properties of P(κ, κ′). Although the contributions P(κ, κ′) obtained by using this procedure are not unique, the results obtained by using various assumptions do not differ significantly. It seems clear from the results that for a region where the energy entering a wavenumber band dominates that leaving, much of the energy entering the band comes from wavenumbers which are about an order of magnitude smaller. That is, the energy transfer is rather nonlocal. This result is not significantly dependent on Reynolds number (for turbulence Reynolds numbers based on microscale from 3 to 800). For lower wavenumbers, where more energy leaves than enters a wavenumber band, the energy transfer into the band is more local, but much of the energy then leaves at distant wavenumbers.