A POD-based analysis of turbulence in the reduced nonlinear dynamics system

Nikolaidis, Marios-Andreas; Farrell, Brian F.; Ioannou, Petros J.; Gayme, Dennice F.; Lozano-Durán, Adrián; Jiménez, Javier

doi:10.1088/1742-6596/708/1/012002

Cited by 10 publications

(14 citation statements)

References 16 publications

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“…The table, while not an exhaustive compilation of existing works on the topic, hints at a lack of consensus on which is the prevailing linear mechanism responsible for the energy transfer from the streaky mean flow to the fluctuations, or if any, it implies that the dominant idea is that exponential instability is the one responsible. We show in this work that the latter is not the case; modal instabilities of the mean streamwise flow are Linear mechanism for ( y, z)-dependent base flow u x Malkus (1956) NEU Schoppa & Hussain (2002) T G Kim et al (1971) EXP (V) Hoepffner et al (2005) TG & EXP (S) Skote et al (2002) EXP Landahl (1990) TG Thomas et al (2015) T G P A R A Lee et al (1990) T G F a r r e l l et al Reddy & Henningson (1993) TG Nikolaidis et al (2016) T G P A R A Butler & Farrell (1993) TG Swearingen & Blackwelder (1987) EXP (S) Trefethen et al (1993) T Cossu et al (2009) TG Park & Huerre (1995) EXP (S) Pujals et al (2009) TG Hamilton et al (1995) Wang et al (2007) EXP (S) Hall & Sherwin (2010) N E U Deguchi et al (2013) N E U Deguchi & Hall (2015) N E U Hall (2018) N E U Table 1. Proposed linear mechanisms responsible for the energy transfer from the base flow to fluctuations for: left columns, y-dependent base flows (primary linear process); right columns, ( y, z)-dependent base flows (secondary linear process).…”

Section: Linear Theories Of Self-sustaining Wall Turbulencementioning

confidence: 77%

“…The works by Kim et al (1971), Swearingen & Blackwelder (1987), Bottaro & Klingmann (1996) and Asai et al (2002) are laboratory experiments, whereas the remainder are numerical investigations. Farrell & Ioannou (2012), Thomas et al (2015), Farrell et al (2016) and Nikolaidis et al (2016) not crucial for self-sustaining turbulence. Next, we briefly describe mechanisms (i), (ii) and (iii).…”

Section: Linear Theories Of Self-sustaining Wall Turbulencementioning

confidence: 98%

“…Finally, mechanism (iii), transient growth assisted by parametric instability, has been advanced in recent years by Farrell, Ioannou & coworkers (Farrell & Ioannou 1999, 2017, 2012Farrell et al 2016Farrell et al , 2017aNikolaidis et al 2016;Bretheim, Meneveau & Gayme 2018). They adopted the perspective of statistical state dynamics (SSD) to develop a tractable theory for the maintenance of wall turbulence.…”

Section: Linear Theories Of Self-sustaining Wall Turbulencementioning

confidence: 99%

“…2016, 2017 a ; Nikolaidis et al. 2016; Bretheim, Meneveau & Gayme 2018). They adopted the perspective of statistical state dynamics (SSD) to develop a tractable theory for the maintenance of wall turbulence.…”

Section: Introductionmentioning

confidence: 99%

“…(2016) and Nikolaidis et al. (2016) are carried out in the context of restricted nonlinear Navier–Stokes. Additionally, some works focus on the buffer layer, logarithmic layer or outer layer.…”

Section: Introductionmentioning

confidence: 99%

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Cause-and-effect of linear mechanisms sustaining wall turbulence

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Section: Linear Theories Of Self-sustaining Wall Turbulencementioning

confidence: 77%

Section: Linear Theories Of Self-sustaining Wall Turbulencementioning

confidence: 98%

Section: Linear Theories Of Self-sustaining Wall Turbulencementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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DNS and POD Analysis of Separated Flow in a Three-Dimensional Diffuser

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et al. 2023

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A statistical state dynamics-based study of the structure and mechanism of large-scale motions in plane Poiseuille flow

et al. 2016

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A. (2016) 'A statistical state dynamics-based study of the structure and mechanism of largescale motions in plane Poiseuille flow', The perspective of statistical state dynamics (SSD) has recently been applied to the study of mechanisms underlying turbulence in a variety of physical systems. An SSD is a dynamical system that evolves a representation of the statistical state of the system. An example of an SSD is the second order cumulant closure referred to as stochastic structural stability theory (S3T), which has provided insight into the dynamics of wall turbulence, and specifically the emergence and maintenance of the roll/streak structure. S3T comprises a coupled set of equations for the streamwise mean and perturbation covariance, in which nonlinear interactions among the perturbations has been removed, restricting nonlinearity in the dynamics to that of the mean equation and the interaction between the mean and perturbation covariance. In this work, this quasi-linear restriction of the dynamics is used to study the structure and dynamics of turbulence in plane Poiseuille flow at moderately high Reynolds numbers in a closely related dynamical system, referred to as the restricted non-linear (RNL) system. Simulations using this RNL system reveal that the essential features of wall-turbulence dynamics are retained. Consistent with previous analyses based on the S3T version of SSD, the RNL system spontaneously limits the support of its turbulence to a small set of streamwise Fourier components giving rise to a naturally minimal representation of its turbulence dynamics. Although greatly simplified, this RNL turbulence exhibits natural-looking structures and statistics albeit with quantitative differences from those in direct numerical simulations (DNS) of the full equations. Surprisingly, even when further truncation of the perturbation support to a single streamwise component is imposed, the RNL system continues to self-sustain turbulence with qualitatively realistic structure and dynamic properties. RNL turbulence at the Reynolds numbers studied is dominated by the roll/streak structure in the buffer layer and similar very-large-scale structure (VLSM) in the outer layer. In this work, diagnostics of the structure, spectrum and energetics of RNL and DNS turbulence are used to demonstrate that the roll/streak dynamics supporting the turbulence in the buffer and logarithmic layer is essentially similar in RNL and DNS. † Email address for correspondence: pjioannou@phys.uoa.gr arXiv:1512.06018v4 [physics.flu-dyn]

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A POD-based analysis of turbulence in the reduced nonlinear dynamics system

Cited by 10 publications

References 16 publications

Cause-and-effect of linear mechanisms sustaining wall turbulence

Cause-and-effect of linear mechanisms sustaining wall turbulence

DNS and POD Analysis of Separated Flow in a Three-Dimensional Diffuser

A statistical state dynamics-based study of the structure and mechanism of large-scale motions in plane Poiseuille flow

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