Instability of the roll-streak structure induced by background turbulence in pretransitional Couette flow

Farrell, Brian F.; Ioannou, Petros J.; Nikolaidis, Marios-Andreas

doi:10.1103/physrevfluids.2.034607

Cited by 14 publications

(35 citation statements)

References 48 publications

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“…Refs. [9,51]). One can compare this behavior to that of the corresponding Navier-Stokes (NS) solutions by defining the N ensemble nonlinear system (NL N ) in analogy with RNL N as follows:…”

Section: Using S3t To Obtain Analytical Solutions For Turbulent Statesmentioning

confidence: 99%

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A statistical state dynamics approach to wall turbulence

Farrell

Gayme

Ioannou

2017

Phil. Trans. R. Soc. A.

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One contribution of 14 to a theme issue 'Toward the development of high-fidelity models of wall turbulence at large Reynolds number' . This paper reviews results obtained using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach used in this work employs a second-order closure that retains only the interaction between the streamwise mean flow and the streamwise mean perturbation covariance. This closure restricts nonlinearity in the SSD to that explicitly retained in the streamwise constant mean flow together with nonlinear interactions between the mean flow and the perturbation covariance. This dynamical restriction, in which explicit perturbation-perturbation nonlinearity is removed from the perturbation equation, results in a simplified dynamics referred to as the restricted nonlinear (RNL) dynamics. RNL systems, in which a finite ensemble of realizations of the perturbation equation share the same mean flow, provide tractable approximations to the SSD, which is equivalent to an infinite ensemble RNL system. This infinite ensemble system, referred to as the stochastic structural stability theory system, introduces new analysis tools for studying turbulence. RNL systems provide computationally efficient means to approximate the SSD and produce self-sustaining turbulence exhibiting qualitative features similar to those observed in direct numerical simulations despite greatly simplified dynamics. The results presented show that RNL turbulence can be supported by as few as a single streamwise varying component interacting with the streamwise constant mean flow and that judicious selection of this truncated support or 'bandlimiting' can be used to improve quantitative accuracy of RNL turbulence. These results suggest that the SSD

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Section: Using S3t To Obtain Analytical Solutions For Turbulent Statesmentioning

confidence: 99%

“…Refs. [22,51]). With continued increase in ε a second bifurcation occurs in which the flow transitions to a chaotic time-dependent state.…”

Section: Using S3t To Obtain Analytical Solutions For Turbulent Statesmentioning

confidence: 99%

A statistical state dynamics approach to wall turbulence

Farrell

Gayme

Ioannou

2017

Phil. Trans. R. Soc. A.

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“…It has been confirmed that this RNL system supports a realistic self-sustaining process (SSP) which maintains a turbulent state in minimal channels [3,4], in channels of moderate sizes at both low and high Reynolds numbers (at least for R τ ≤ 1000) [5][6][7], and also in very long channels [8].…”

Section: Introductionmentioning

confidence: 56%

“…We instead calculate only the Lyapunov exponents and structures of perturbations, u , evolving under the linear dynamics (4) with time dependent mean flow U . It is important to recognize that the parametric perturbation evolution equation (4) governing the perturbation Lyapunov vector dynamics of RNL is not limited to small perturbation amplitude and the nonlinearity required to regulate the perturbations to their finite statistical equilibrium state, although not present in (4), is contained in the Reynolds stress feedback term N 2 appearing in the mean equation.…”

Section: Introductionmentioning

confidence: 99%

The mechanism by which nonlinearity sustains turbulence in plane Couette flow

Nikolaidis

Farrell

Ioannou

2018

J. Phys.: Conf. Ser.

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Turbulence in wall-bounded shear flow results from a synergistic interaction between linear non-normality and nonlinearity in which non-normal growth of a subset of perturbations configured to transfer energy from the externally forced component of the turbulent state to the perturbation component maintains the perturbation energy, while the subset of energytransferring perturbations is replenished by nonlinearity. Although it is accepted that both linear non-normality mediated energy transfer from the forced component of the mean flow and nonlinear interactions among perturbations are required to maintain the turbulent state, the detailed physical mechanism by which these processes interact in maintaining turbulence has not been determined. In this work a statistical state dynamics based analysis is performed on turbulent Couette flow at R = 600 and a comparison to DNS is used to demonstrate that the perturbation component in Couette flow turbulence is replenished by a non-normality mediated parametric growth process in which the fluctuating streamwise mean flow has been adjusted to marginal Lyapunov stability. It is further shown that the alternative mechanism in which the subspace of non-normally growing perturbations is maintained directly by perturbation-perturbation nonlinearity does not contribute to maintaining the turbulent state. This work identifies parametric interaction between the fluctuating streamwise mean flow and the streamwise varying perturbations to be the mechanism of the nonlinear interaction maintaining the perturbation component of the turbulent state, and identifies the associated Lyapunov vectors with positive energetics as the structures of the perturbation subspace supporting the turbulence.

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“…1993; Farrell & Ioannou 1996; Del Álamo & Jiménez 2006; Schmid 2007; Cossu, Pujals & Depardon 2009). Other studies suggest that the generation of streaks is due to the structure-forming properties of the linearised Navier–Stokes operator, independent of any organised vortices (Chernyshenko & Baig 2005), or due to the interaction of the background free-stream turbulence and the roll-streak structures (Farrell, Ioannou & Nikolaidis 2017 b ), but the non-modal nature of the linear operator is still crucially invoked. Input–output analysis of the linearised Navier–Stokes equations has also been successful in characterising the non-modal response of the base flow (Farrell & Ioannou 1993 b ; Jovanović & Bamieh 2005; Hwang & Cossu 2010 a ; Zare et al.…”

Section: Introductionmentioning

confidence: 99%