Dual spectra and mixed energy cascade of turbulence in the wavelet representation

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Abstract
The wavelet-transformed Navier-Stokes equations are used to define quantities such as the transfer and flux of kinetic energy through position x and scale r. Analysis of pseudospectral direct numerical simulations of turbulent flows reveals that although the mean spatial values of these quantities agree with their traditional counterparts in Fourier space, their spatial variability is very large, exhibiting non-Gaussian statistics. The local flux of energy involving scales smaller than some r also exhibits large spatial intermittency and it is negative quite often, indicative of local inverse cascades.

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