Intermittency-Driven Turbulence Cascade Memory Extends the Markov-Einstein Coherence Length Beyond the Canonical Estimate
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915960589385728 |
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| author | Ju, Y. Sungtaek |
| author_facet | Ju, Y. Sungtaek |
| contents | Using direct numerical simulation of forced isotropic turbulence at $\text{Re}_λ\approx 1300$ and $\approx 433$, together with two independent Markov-by-construction null surrogates, we measure the Markov--Einstein coherence length of the turbulent energy cascade to be $Δr \approx 3.2$-$3.6$ in log-scale cascade coordinates, approximately three times the canonical estimate $Δr \approx 1$. Stratifying the gap-scan test by local dissipation intensity and by increment amplitude reveals that intermittent events carry $Δr \approx 3$-$4$, while at mid-inertial-range scales the quiescent cascade recovers $Δr \approx 1.0$-$1.4$, consistent with the canonical value. Near the dissipation range this pattern reverses: bulk dynamics carry more memory than extreme events, consistent with the spectral bottleneck. The excess memory is internal to the inertial range and Reynolds-number-independent over $\text{Re}_λ\approx 433$-$1300$. These findings indicate that the Markov approximation underlying the cascade Fokker-Planck equation and fluctuation-theorem analyses is substantially more restrictive than previously assumed, and that a non-Markovian correction, informed by the amplitude-dependent memory structure identified here, is needed for the intermittent component of the cascade. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_23962 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Intermittency-Driven Turbulence Cascade Memory Extends the Markov-Einstein Coherence Length Beyond the Canonical Estimate Ju, Y. Sungtaek Fluid Dynamics Data Analysis, Statistics and Probability Using direct numerical simulation of forced isotropic turbulence at $\text{Re}_λ\approx 1300$ and $\approx 433$, together with two independent Markov-by-construction null surrogates, we measure the Markov--Einstein coherence length of the turbulent energy cascade to be $Δr \approx 3.2$-$3.6$ in log-scale cascade coordinates, approximately three times the canonical estimate $Δr \approx 1$. Stratifying the gap-scan test by local dissipation intensity and by increment amplitude reveals that intermittent events carry $Δr \approx 3$-$4$, while at mid-inertial-range scales the quiescent cascade recovers $Δr \approx 1.0$-$1.4$, consistent with the canonical value. Near the dissipation range this pattern reverses: bulk dynamics carry more memory than extreme events, consistent with the spectral bottleneck. The excess memory is internal to the inertial range and Reynolds-number-independent over $\text{Re}_λ\approx 433$-$1300$. These findings indicate that the Markov approximation underlying the cascade Fokker-Planck equation and fluctuation-theorem analyses is substantially more restrictive than previously assumed, and that a non-Markovian correction, informed by the amplitude-dependent memory structure identified here, is needed for the intermittent component of the cascade. |
| title | Intermittency-Driven Turbulence Cascade Memory Extends the Markov-Einstein Coherence Length Beyond the Canonical Estimate |
| topic | Fluid Dynamics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2604.23962 |