State-dependent Markov memory in the turbulent energy cascade

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Abstract
The turbulent energy cascade is widely modeled as a Markov process in scale, valid above a coherence length of about one Taylor microscale. Using direct numerical simulation results and null surrogates that are Markov by construction, the present work shows that this coherence length is state dependent: quiescent regions of the inertial range recover the canonical value, while intermittent regions require 3 to 4 times the scale separation, and the ordering reverses near the dissipation range. The Markov approximation underlying cascade Fokker-Planck and fluctuation-theorem analyses is therefore more restrictive for the intermittent component of the cascade than has generally been assumed.

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