Perturbation Structure and Spectra in Turbulent Channel Flow

Farrell, Brian F.; Ioannou, Petros J.

doi:10.1007/s001620050091

Cited by 45 publications

(30 citation statements)

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“…All of these studies demonstrate encouraging agreement between predictions resulting from stochastically driven linearized models and available data and highlight the challenges that arise in modeling dissipation and the statistics of forcing (DelSole 2000(DelSole , 2004. Farrell & Ioannou (1998) examined the statistics of the NS equations linearized around the Reynolds-Tiederman velocity profile subject to white stochastic forcing. It was demonstrated that velocity correlations over a finite interval determined by the eddy turnover time qualitatively agree with second-order statistics of turbulent channel flow.…”

Section: Stochastic Forcing and Flow Statisticsmentioning

confidence: 81%

“…Furthermore, Chernyshenko & Baig (2005) used the linearized NS equations to predict the spacing of near-wall streaks and relate their formation to a combination of lift-up due to the mean profile, mean shear, and viscous dissipation. The linearized NS equations also reveal large transient growth of fluctuations around turbulent mean velocity (Butler & Farrell 1993;Farrell & Ioannou 1993a) and a high amplification of stochastic disturbances (Farrell & Ioannou 1998). Schoppa & Hussain (2002) ;Hoepffner, Brandt & Henningson (2005a) further identified a secondary growth (of the streaks) which may produce much larger transient responses than a secondary instability.…”

Section: Linear Analysis Of Transitional and Turbulent Shear Flowsmentioning

confidence: 86%

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Colour of turbulence

2017

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In this paper, we address the problem of how to account for second-order statistics of turbulent flows using low-complexity stochastic dynamical models based on the linearized Navier-Stokes equations. The complexity is quantified by the number of degrees of freedom in the linearized evolution model that are directly influenced by stochastic excitation sources. For the case where only a subset of velocity correlations are known, we develop a framework to complete unavailable second-order statistics in a way that is consistent with linearization around turbulent mean velocity. In general, white-in-time stochastic forcing is not sufficient to explain turbulent flow statistics. We develop models for colored-intime forcing using a maximum entropy formulation together with a regularization that serves as a proxy for rank minimization. We show that colored-in-time excitation of the Navier-Stokes equations can also be interpreted as a low-rank modification to the generator of the linearized dynamics. Our method provides a data-driven refinement of models that originate from first principles and captures complex dynamics of turbulent flows in a way that is tractable for analysis, optimization, and control design.

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Section: Stochastic Forcing and Flow Statisticsmentioning

confidence: 81%

Section: Linear Analysis Of Transitional and Turbulent Shear Flowsmentioning

confidence: 86%

Colour of turbulence

2017

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“…Attempts have been made to use linear analysis to explain the dominant features of turbulent flow in terms of optimal transient modes 5, 10 or stochastic forcing. 11,12 The present analysis is closer to a resolvent or system norm analysis. 13,14 A different approach by other authors [15][16][17] has developed exact solutions of the Navier-Stokes equations, giving rise to unstable coherent structures, as the foundations of transitional flow and/or near-wall turbulence.…”

Section: A Non-normality and Algebraic Disturbance Growthmentioning

confidence: 87%

Perturbation Energy Production in Pipe Flow over a Range of Reynolds Numbers using Resolvent Analysis

Sharma

McKeon

2009

47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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The response of pipe flow to physically realistic, temporally and spatially continuous (periodic) forcing is investigated by decomposing the resolvent into orthogonal forcing and response pairs ranked according to their contribution to the resolvent 2-norm. Modelling the non-linear terms normally neglected by linearisation as unstructured forcing permits qualitative extrapolation of the resolvent norm results beyond infinitesimally small perturbations to the turbulent case. The concepts arising have a close relationship to inputoutput transfer function analysis methods known in the control systems literature. The body forcings that yield highest disturbance energy gain are identified and ranked by the decomposition and a worst-case bound put on the energy gain integrated across the pipe cross-section. Analysis of the spectral variation of the corresponding response modes reveals interesting comparisons with recent observations of the behavior of the streamwise velocity in high Reynolds number (turbulent) pipe flow, including the importance of very long scales of the order of ten pipe radii, in the extraction of turbulent energy from the mean flow by the action of turbulent shear stress against the velocity gradient.

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“…Relevance of the stochastic forcing analysis When trying to relate the results of the present analysis to experimental observations of unforced turbulent flows, considering stochastic forcing is probably more relevant than considering harmonic forcing. In the spirit of Farrell & Ioannou (1994) and Farrell & Ioannou (1998), the stochastic forcing can be assumed to be a surrogate for the nonlinear terms that are neglected in the linearized model. The distribution V (α, β) would then represent the linear amplification of the variance of the nonlinear terms, where the whole variance integrated in the wall-normal direction is considered.…”

Section: Discussionmentioning

confidence: 99%

“…The use of pre-multiplied energy amplifications allows us then to analyse the deviations from the β-power-law behaviour and to identify the spanwise scales associated to the most amplified structures in the near wall and at large scales. Previous similar investigations have not detected the approximate β-power scaling of the amplifications of log-layer structures, either because the molecular viscosity instead of the turbulent eddy viscosity was used in the linearized equations (Farrell & Ioannou 1998) or because a too low Reynolds number was considered ). This paper is organized as follows: in § 2, we briefly introduce the considered turbulent mean base flow, the associated eddy viscosity and the equations satisfied by small coherent perturbations to the base flow.…”

Section: Introductionmentioning

confidence: 99%

Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow

2010

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To cite this version:Yongyun Hwang, Carlo Cossu. Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2010, 664 (December), pp. 51-73. 10.1017/s0022112010003629. hal-01020668 J. Fluid Mech. (2010 The linear response to stochastic and optimal harmonic forcing of small coherent perturbations to the turbulent channel mean flow is computed for Reynolds numbers ranging from Re τ = 500 to 20 000. Even though the turbulent mean flow is linearly stable, it is nevertheless able to sustain large amplifications by the forcing. The most amplified structures consist of streamwise-elongated streaks that are optimally forced by streamwise-elongated vortices. For streamwise-elongated structures, the mean energy amplification of the stochastic forcing is found to be, to a first approximation, inversely proportional to the forced spanwise wavenumber while it is inversely proportional to its square for optimal harmonic forcing in an intermediate spanwise wavenumber range. This scaling can be explicitly derived from the linearized equations under the assumptions of geometric similarity of the coherent perturbations and of logarithmic base flow. Deviations from this approximate power-law regime are apparent in the pre-multiplied energy amplification curves that reveal a strong influence of two different peaks. The dominant peak scales in outer units with the most amplified spanwise wavelength of λ z ≈ 3.5h, while the secondary peak scales in wall units with the most amplified λ + z ≈ 80. The associated optimal perturbations are almost independent of the Reynolds number when, respectively, scaled in outer and inner units. In the intermediate wavenumber range, the optimal perturbations are approximatively geometrically similar. Furthermore, the shape of the optimal perturbations issued from the initial value, the harmonic forcing and the stochastic forcing analyses are almost indistinguishable. The optimal streaks corresponding to the large-scale peak strongly penetrate into the inner layer, where their amplitude is proportional to the mean-flow profile. At the wavenumbers corresponding to the large-scale peak, the optimal amplifications of harmonic forcing are at least two orders of magnitude larger than the amplifications of the variance of stochastic forcing and both increase with the Reynolds number. This confirms the potential of the artificial forcing of optimal large-scale streaks for the flow control of wall-bounded turbulent flows.

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Perturbation Structure and Spectra in Turbulent Channel Flow

Cited by 45 publications

References 31 publications

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Perturbation Energy Production in Pipe Flow over a Range of Reynolds Numbers using Resolvent Analysis

Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow

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