Synchronization of low Reynolds number plane Couette turbulence

Nikolaidis, Marios-Andreas; Ioannou, Petros J.

doi:10.1017/jfm.2021.1054

Cited by 6 publications

(11 citation statements)

References 38 publications

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“…It is known that for canonical chaotic systems, synchronisation occurs only when the CLE is negative (Boccaletti et al 2002). The same is confirmed for turbulent channel flows (Nikolaidis & Ioannou 2022). One of the questions to be addressed in the present investigation is how the CLE λ(k m ) depends on the Rossby number.…”

Section: Governing Equationssupporting

confidence: 58%

The conditional Lyapunov exponents and synchronisation of rotating turbulent flows

Li,

Tian,

et al. 2024

J. Fluid Mech.

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The synchronisation between rotating turbulent flows in periodic boxes is investigated numerically. The flows are coupled via a master–slave coupling, taking the Fourier modes with wavenumber below a given value $k_m$ as the master modes. It is found that synchronisation happens when $k_m$ exceeds a threshold value $k_c$ , and $k_c$ depends strongly on the forcing scheme. In rotating Kolmogorov flows, $k_c\eta$ does not change with rotation in the range of rotation rates considered, $\eta$ being the Kolmogorov length scale. Even though the energy spectrum has a steeper slope, the value of $k_c\eta$ is the same as that found in isotropic turbulence. In flows driven by a forcing term maintaining constant energy injection rate, synchronisation becomes easier when rotation is stronger. Here, $k_c\eta$ decreases with rotation, and it is reduced significantly for strong rotations when the slope of the energy spectrum approaches $-3$ . It is shown that the conditional Lyapunov exponent for a given $k_m$ is reduced by rotation in the flows driven by the second type of forcing, but it increases mildly with rotation for the Kolmogorov flows. The local conditional Lyapunov exponents fluctuate more strongly as rotation is increased, although synchronisation occurs as long as the average conditional Lyapunov exponents are negative. We also look for the relationship between $k_c$ and the energy spectra of the Lyapunov vectors. We find that the spectra always seem to peak at approximately $k_c$ , and synchronisation fails when the energy spectra of the conditional Lyapunov vectors have a local maximum in the slaved modes.

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Section: Governing Equationssupporting

confidence: 58%

The conditional Lyapunov exponents and synchronisation of rotating turbulent flows

Li,

Tian,

et al. 2024

J. Fluid Mech.

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“…2020). Nikolaidis & Ioannou (2022) investigated synchronization in plane Couette flow by enforcing streamwise low wavenumber modes and obtained a similar criterion as in isotropic turbulence. No previous study has examined synchronization of wall turbulence in physical space or explored the anisotropy of the synchronization criterion along different flow directions.…”

Section: Introductionmentioning

confidence: 97%

“…This criterion is independent of the data assimilation techniques adopted, including direct substitution (Yoshida et al 2005), nudging (Clark Di Leoni, Mazzino & Biferale 2020) or adjoint-variational methods (Li et al 2020). Nikolaidis & Ioannou (2022) investigated synchronization in plane Couette flow by enforcing streamwise low wavenumber modes and obtained a similar criterion as in isotropic turbulence. No previous study has examined synchronization of wall turbulence in physical space or explored the anisotropy of the synchronization criterion along different flow directions.…”

mentioning

confidence: 99%

Synchronization of turbulence in channel flow

Wang

Zaki

2022

J. Fluid Mech.

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Synchronization of turbulence in channel flow is investigated using continuous data assimilation. The flow is unknown within a region of the channel. Beyond this region the velocity field is provided, and is directly prescribed in the simulation, while the pressure is unknown throughout the entire domain. Synchronization takes place when the simulation recovers the full true state of the flow, or in other words when the missing region is accurately re-established, spontaneously. Successful synchronization depends on the orientation, location and size of the missing layer. For friction Reynolds numbers up to one thousand, wall-attached horizontal layers can synchronize as long as their thickness is less than approximately thirty wall units. When the horizontal layer is detached from the wall, the critical thickness increases with height and is proportional to the local wall-normal Taylor microscale. A flow-parallel, vertical layer that spans the height of the channel synchronizes when its spanwise width is of the order of the near-wall Taylor microscale, while the criterion for a crossflow vertical layer is set by the advection distance within a Lyapunov time scale. Finally, we demonstrate that synchronization is possible when only planar velocity data are available, rather than the full outer state, as long as the unknown region satisfies the condition for synchronization in one direction. These numerical experiments demonstrate the capacity of accurately reconstructing, or synchronizing, the missing scales of turbulence from observations, using continuous data assimilation.

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“…It is important to recognize that this restriction in the support of RNL turbulence to a small subset of streamwise Fourier components is not imposed but rather is a property of the dynamics with significant implication. The components that are retained spontaneously by the RNL dynamics identify the streamwise harmonics that are dynamically active in the sense that this subset of streamwise harmonics participates in the parametric instability that sustains the fluctuation component of the turbulent state (Farrell & Ioannou 2012Thomas et al 2014Thomas et al , 2015Nikolaidis & Ioannou 2022). The data were obtained from DNS of (2.1) and from simulation of the associated RNL system governed by (2.2).…”

Section: Dns and Their Rnl Approximationmentioning

confidence: 99%

“…The components that are retained spontaneously by the RNL dynamics identify the streamwise harmonics that are dynamically active in the sense that this subset of streamwise harmonics participates in the parametric instability that sustains the fluctuation component of the turbulent state (Farrell & Ioannou 2012, 2017; Thomas et al. 2014, 2015; Nikolaidis & Ioannou 2022).…”

Section: Dns and Their Rnl Approximationmentioning

confidence: 99%

POD-based study of turbulent plane Poiseuille flow: comparing structure and dynamics between quasi-linear simulations and DNS

et al. 2023

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Turbulence in the restricted nonlinear (RNL) dynamics is analysed and compared with direct numerical simulations (DNS) of Poiseuille turbulence at Reynolds number $R=1650$ . The structures are obtained by proper orthogonal decomposition (POD) analysis of the two components of the flow partition used in RNL dynamics: the streamwise mean flow and fluctuations. POD analysis of the streamwise mean flow indicates that the dominant POD modes, in both DNS and RNL dynamics, are roll-streaks harmonic in the spanwise direction. However, we conclude that these POD modes do not occur in isolation but rather are Fourier components of a coherent roll-streak structure. POD analysis of the fluctuations in DNS and RNL dynamics reveals similar complex structures consisting in part of oblique waves collocated with the streak. The origin of these structures is identified by their correspondence to POD modes predicted using a stochastic turbulence model (STM). These predicted POD modes are dominated by the optimally growing structures on the streak, which the STM predicts correctly to be of sinuous oblique wave structure. This close correspondence between the roll-streak structure and the associated fluctuations in DNS, RNL dynamics and the STM implies that the self-sustaining mechanism operating in DNS is essentially the same as that in RNL dynamics, which has been associated previously with optimal perturbation growth on the streak.

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Synchronization of low Reynolds number plane Couette turbulence

Cited by 6 publications

References 38 publications

The conditional Lyapunov exponents and synchronisation of rotating turbulent flows

The conditional Lyapunov exponents and synchronisation of rotating turbulent flows

Synchronization of turbulence in channel flow

POD-based study of turbulent plane Poiseuille flow: comparing structure and dynamics between quasi-linear simulations and DNS

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