A note on optimal transient growth in turbulent channel flows

Pujals, Grégory; García-Villalba, Manuel; Cossu, Carlo; Depardon, S.

doi:10.1063/1.3068760

Cited by 166 publications

(299 citation statements)

References 24 publications

(47 reference statements)

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“…The selfsustaining process was also found to be almost identical to that in the near-wall region: 1) the streaky structure (VLSM) is amplified by the vortical structures (LSMs) via the lift-up effect (e.g. Cossu et al 2009;Pujals et al 2009;Hwang & Cossu 2010a;Willis et al 2010); 2) the amplified streak undergoes rapid streak meandering motion via secondary instability or transient growth (Park et al 2011); 3) the following nonlinear regeneration of the streamwise vortical structures (Hwang & Bengana 2016).…”

Section: Introductionmentioning

confidence: 88%

Invariant solutions of minimal large-scale structures in turbulent channel flow for up to 1000

2016

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Understanding the origin of large-scale structures in high Reynolds number wall turbulence has been a central issue over a number of years. Recently, Rawat et al. (J. Fluid Mech., 2015, 782, p515) have computed invariant solutions for the large-scale structures in turbulent Couette flow at Re τ ≃ 128 using an over-damped LES with the Smagorinsky model to account for the effect of the surrounding small-scale motions. Here, we extend this approach to an order of magnitude higher Reynolds numbers in turbulent channel flow, towards the regime where the large-scale structures in the form of very-large-scale motions (long streaky motions) and large-scale motions (short vortical structures) energetically emerge. We demonstrate that a set of invariant solutions can be computed from simulations of the self-sustaining large-scale structures in the minimal unit (domain of size L x = 3.0h streamwise and L z = 1.5h spanwise) with midplane reflection symmetry at least up to Re τ ≃ 1000. By approximating the surrounding small scales with an artificially elevated Smagorinsky constant, a set of equilibrium states are found, labelled upper-and lower-branch according to their associated drag. It is shown that the upper-branch equilibrium state is a reasonable proxy for the spatial structure and the turbulent statistics of the self-sustaining large-scale structures.

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Section: Introductionmentioning

confidence: 88%

Invariant solutions of minimal large-scale structures in turbulent channel flow for up to 1000

2016

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“…The main (outer) peak scales in outer units and roughly corresponds to large-scale streaky motions in the outer region. The associated maximum energy growth increases proportionally to a Reynolds number based on outer units Re out = U c δ/ν T,max [26,32]. The secondary (inner) peak scales in inner (wall) units and corresponds to λ + z ≈ 90 [26,31,32,34], i.e.…”

Section: The Coherent Lift-up Effectmentioning

confidence: 99%

“…The spanwise wavelength is scaled in outer (λ z /h) and wall units (λ + z = λ z u τ /ν), respectively, in panels (a) and (b). (Adapted from channel flow data reported in [26,27].) (Online version in colour.…”

Section: The Coherent Lift-up Effectmentioning

confidence: 99%

“…Important progress was made by using the generalized Orr-Sommerfeld and Squire operators, which include a non-uniform eddy viscosity ν T (y) associated with the turbulent mean flow used to model the turbulent Reynolds stresses. 1 An incorrect early expression of these operators [31] has been amended in later studies [26,32] to…”

Section: The Coherent Lift-up Effectmentioning

confidence: 99%

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Self-sustaining processes at all scales in wall-bounded turbulent shear flows

Cossu

Hwang

2017

Phil. Trans. R. Soc. A.

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We collect and discuss the results of our recent studies which show evidence of the existence of a whole family of self-sustaining motions in wall-bounded turbulent shear flows with scales ranging from those of buffer-layer streaks to those of large-scale and very-large-scale motions in the outer layer. The statistical and dynamical features of this family of self-sustaining motions, which are associated with streaks and quasi-streamwise vortices, are consistent with those of Townsend’s attached eddies. Motions at each relevant scale are able to sustain themselves in the absence of forcing from larger- or smaller-scale motions by extracting energy from the mean flow via a coherent lift-up effect. The coherent self-sustaining process is embedded in a set of invariant solutions of the filtered Navier–Stokes equations which take into full account the Reynolds stresses associated with the residual smaller-scale motions. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

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“…Luchtenburg et al (2009);Östh et al (2014); Protas et al (2015). Mean flow stability has been used for many studies of convective instability (including the seminal works of Gaster et al 1985, Weisbrot & Wygnanski 1988, Cohen & Wygnanski 1987 and transient growth (Hoyas & Jimenez 2006;Pujals et al 2009). Here, we will focus on the oscillator behaviour and, in particular, its adjoint-based sensitivity.…”

Section: Introductionmentioning

confidence: 99%

Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes

2016

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The large-scale coherent motions in a realistic swirl fuel injector geometry are analysed by direct numerical simulations (DNS), proper orthogonal decomposition (POD), and linear global modes. The aim is to identify the origin of instability in this turbulent flow in a complex internal geometry.The flow field in the nonlinear simulation is highly turbulent, but with a distinguishable coherent structure: the precessing vortex core (a spiraling mode).The most energetic POD mode pair is identified as the precessing vortex core. By analysing the FFT of the time coefficients of the POD modes, we conclude that the first four POD modes contain the coherent fluctuations. The remaining POD modes (incoherent fluctuations) are used to form a turbulent viscosity field, using the Newtonian eddy model.The turbulence sets in from convective shear layer instabilities even before the nonlinear flow reaches the other end of the domain, indicating that equilibrium solutions of the Navier-Stokes are never observed. Linear global modes are computed around the mean flow from DNS, applying the turbulent viscosity extracted from POD modes. A slightly stable discrete m = 1 eigenmode is found, well separated from the continuous spectrum, in very good agreement with the POD mode shape and frequency. The structural sensitivity of the precessing vortex core is located upstream of the central recirculation zone, identifying it as a spiral vortex breakdown instability in the nozzle. Furthermore, the structural sensitivity indicates that the dominant instability mechanism is the KelvinHelmholtz instability at the inflection point forming near vortex breakdown. Adjoint modes are strong in the shear layer along the whole extent of the nozzle, showing that the optimal initial condition for the global mode is localized in the shear layer.We analyse the qualitative influence of turbulent dissipation in the stability problem (eddy viscosity) on the eigenmodes by comparing them to eigenmodes computed without eddy viscosity. The results show that the eddy viscosity improves the complex frequency and shape of global modes around the fuel injector mean flow, while a qualitative wavemaker position can be obtained with or without turbulent dissipation, in agreement with previous studies.This study shows how sensitivity analysis can identify which parts of the flow in a complex geometry need to be altered in order to change its hydrodynamic stability characteristics.Key Words: † Email address for correspondence: outi-leena.tammisola@nottingham.ac.uk , and the exit velocity from the swirler (U E ). The coordinate system is also defined: the origin is at the centerline at the swirler exit location. The relative dimensions of the geometry are the same as in the numerical simulation, except that the numerical domain is longer in the downstream direction.

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A note on optimal transient growth in turbulent channel flows

Cited by 166 publications

References 24 publications

Invariant solutions of minimal large-scale structures in turbulent channel flow for up to 1000

Invariant solutions of minimal large-scale structures in turbulent channel flow for up to 1000

Self-sustaining processes at all scales in wall-bounded turbulent shear flows

Coherent structures in a swirl injector at Re = 4800 by nonlinear simulations and linear global modes

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