SPECTRA AND FILTERING: A CLARIFICATION
Abstract
Filtering methods have been introduced in the early nineties, in 1988 by Farge et al. for a wavelet filtering, in 1987 by Benzi et al. and in 1994 by Borue for a direct cut-off filtering. The aim of these methods is to filter the velocity and/or the vorticity fields of two-dimensional turbulence experiments in order to enhance the various components of the fluid. Using this king of methods allows us to separate the vortices from the background essentially composed by vorticity filaments. We have also shown the ability of the wavelet packets in performing this filtering. However, we had underestimated, like Borue in 1994, the influence of the filtering process in the computation of the energy and/or enstrophy spectra. We will show in the present paper how the introduction of discontinuities due to the filtering process can subsequently modify the spectra.
