2021
DOI: 10.48550/arxiv.2112.06537
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Aging and memory of transitional turbulence

Abstract: The recent classification of the onset of turbulence as a directed percolation (DP) phase transition has been applied to all major shear flows including pipe, channel, Couette and boundary layer flows. A cornerstone of the DP analogy is the memoryless (Markov) property of turbulent sites. We here show that for the classic case of channel flow, the growth of turbulent stripes is deterministic and that memorylessness breaks down. Consequently turbulence ages and the one to one mapping between turbulent patches a… Show more

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Cited by 6 publications
(19 citation statements)
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“…For large channel domains, however, it is illustrated numerically that the transition starts with a sparse turbulence state, where the localized turbulent bands are sustained by a dynamic balance between band extension and band breaking [31,32]. The lower bound or threshold Reynolds number of the sparse turbulence state is Re c = 660, which is confirmed experimentally by velocity field measurements [33,34] and flow visualizations [35]. Above Re ≈ 700, most turbulent bands are found numerically to have the same orientation and the spanwise symmetry is restored and the two-dimensional directed-percolation is retrieved only above Re ≈ 1000 [36].…”
Section: Introductionmentioning
confidence: 65%
“…For large channel domains, however, it is illustrated numerically that the transition starts with a sparse turbulence state, where the localized turbulent bands are sustained by a dynamic balance between band extension and band breaking [31,32]. The lower bound or threshold Reynolds number of the sparse turbulence state is Re c = 660, which is confirmed experimentally by velocity field measurements [33,34] and flow visualizations [35]. Above Re ≈ 700, most turbulent bands are found numerically to have the same orientation and the spanwise symmetry is restored and the two-dimensional directed-percolation is retrieved only above Re ≈ 1000 [36].…”
Section: Introductionmentioning
confidence: 65%
“…These simulations are well resolved with a resolution of N x = N z =1024 (including dealiasing with the 2/3 rule) comparable to [3]. The most recent investigations have reported laminar-turbulent patterns for 50 Re τ 90, and independent turbulent bands for lower values of Re τ down to ≈ 36 [3,15,22,23].…”
mentioning
confidence: 61%
“…In more realistic channel flow, where turbulence can be fully localized by developing a downstream end and an upstream end, the statistical characteristic of the globally sustained turbulence was proposed to be described by the two-plus-one-dimensional ((2+1)-D) DP model only in a limited range of transitional Reynolds number (Sano & Tamai 2016;Shimizu & Manneville 2019). Recent studies reported that a fully localized turbulent band becomes sustained already at low Reynolds numbers Re cr 650-660 (Kanazawa 2018;Tao, Eckhardt & Xiong 2018;Paranjape 2019;Mukund et al 2021), far below the critical Reynolds numbers of Re cr,DP 830 (Sano & Tamai 2016) and 905 (Shimizu & Manneville 2019) for sustained turbulence in DP theory. This early sustained turbulence conflicts with DP that turbulence should be transient and the flow should eventually laminarize completely when the Reynolds number is below Re cr,DP .…”
Section: Introductionmentioning
confidence: 99%
“…The self-sustaining of a turbulent band is mainly ascribed to turbulence generation at its downstream end (Kanazawa 2018;Paranjape 2019;Shimizu & Manneville 2019;Liu et al 2020;Xiao & Song 2020a,b;Mukund et al 2021). Kanazawa (2018) proposed that a nonlinear relative periodic orbit is embedded at the downstream end of a turbulent band, generating velocity streaks and vortices periodically; while Xiao & Song (2020a) and Song & Xiao (2020) reported an inflectional instability associated with the local mean flow as the mechanism for turbulence generation there.…”
Section: Introductionmentioning
confidence: 99%
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