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In direct numerical simulation of turbulence what is the advantage to look at the spectra of the energy flux rather than the transfer spectra?

The transfer spectra corresponds to the triple-velocity correlation coming from the non-linear interaction of the Navier-Stokes equations. The transfer spectra is generally noted: \begin{equation} T(\mathbf{k},t) \end{equation} The energy flux through wave number $\mathbf{k}$ is defined from the transfer spectra by \begin{equation} \Pi(\mathbf{k},t)=\int^{\infty}_{\mathbf{k}}T(\mathbf{p},t)d\mathbf{p}=-\int^{\mathbf{k}}_{0}T(\mathbf{p},t)d\mathbf{p} \end{equation}

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