Integral-scale intermittency

Integral-scale intermittency is modulation of the energy-containing motions and the energy supply on large lengths or long turnover times. Averaging velocity statistics over regions or realizations with differing viscous dissipation rates can invalidate universal coefficients based only on the global mean viscous dissipation.

Mixing turbulent populations with differing viscous dissipation gives $S_p={\beta }_p{r}^{p/3}⟨{ϵ}_a^{p/3}⟩$. Relative to the same power of the mean viscous dissipation, the coefficient changes with the intensity distribution except at $p=3$. Thus universality of all unconditional coefficients is incompatible with arbitrary integral-scale intermittency.