• Accepted Paper

State-dependent Markov memory in the turbulent energy cascade

Y. Sungtaek Ju

Phys. Rev. Fluids - Accepted 2 September, 2026

DOI: https://doi.org/10.1103/4p16-3qyj

Abstract

Using direct numerical simulation of forced isotropic turbulence at Reλ1300 and 433, 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 Δr34, while the quiescent cascade at mid-inertial scales recovers Δr1.01.4, 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 Δr3.23.6 at the inertial-range centers, approximately three times the canonical reference Δr1. An independent Chapman–Kolmogorov test confirms the state-dependence, and a subsampling test shows the excess is present already at the 105 samples-per-scale regime of the earlier experiments. The pattern is Reynolds-number-independent over Reλ4331300. 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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