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Both are of course connected, but denote very different concepts. Your definition of variance is fine with me. It tells us, on average, how much the flow deviates from its average. Intermittency is much harder to explain. I'll do my best here: In a scale invariant flow, the $n$'th order correlation function will take a scaling form, \Delta\Psi(n,r) = ...

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There is nothing to do. If you force your system strongly, energy will build up and your hydrodynamic flow will become more and more intricate. At the same time, the dissipation becomes more and more efficient since it is proportional to the spatial derivative of the velocity field. You reach a steady state when both effects compensate each other. The ...

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