- Accepted Paper
State-dependent Markov memory in the turbulent energy cascade
Phys. Rev. Fluids - Accepted 2 September, 2026
DOI: https://doi.org/10.1103/4p16-3qyj
Phys. Rev. Fluids - Accepted 2 September, 2026
DOI: https://doi.org/10.1103/4p16-3qyj
Using direct numerical simulation of forced isotropic turbulence at and , together with two independent Markov-in-scale-by-construction null surrogates, we show that the Markov–Einstein coherence length of the turbulent energy cascade is . Conditioning the gap-scan test on the local flow state reveals that intermittent regions of the inertial range carry a coherence length –, while the quiescent cascade at mid-inertial scales recovers –, matching the canonical estimate to within one grid step. Near the dissipation range this pattern reverses: the core of the increment distribution carries more memory than the extreme tails, consistent with the spectral bottleneck. As a consequence, the unconditioned coherence length coincides with that of the intermittent component, whose memory is the last to decay as the scale separation grows and therefore sets the coherence length, giving – at the inertial-range centers, approximately three times the canonical reference . An independent Chapman–Kolmogorov test confirms the state-dependence, and a subsampling test shows the excess is present already at the samples-per-scale regime of the earlier experiments. The pattern is Reynolds-number-independent over –. The Markov approximation underlying the cascade Fokker–Planck equation and fluctuation-theorem analyses is therefore substantially more restrictive for the intermittent component of the cascade than previously assumed.
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