  In his seminal work on turbulence, Kolmogorov made use of the stationary
hypothesis to determine the Power Density Spectrum of the velocity field in
turbulent flows. However to our knowledge, the constraints that stationary
processes impose on the fluctuations of the energy flux have never been used in
the context of turbulence. Here we recall that the Power Density Spectra of the
fluctuations of the injected power, the dissipated power and the energy flux
have to converge to a common value at vanishing frequency. Hence, we show that
the intermittent GOY--shell model fulfills these constraints. We argue that
they can be related to intermittency. Indeed, we find that the constraint on
the fluctuations of the energy flux implies a relation between the scaling
exponents that characterize intermittency, which is verified by the GOY--shell
model and in agreement with the She-Leveque formula. It also fixes the
intermittency parameter of the log-normal model at a realistic value. The
relevance of these results for real turbulence is drawn in the concluding
remarks.
