Nonlinear mechanism of the self-sustaining process in the buffer and logarithmic layer of wall-bounded flows

Bae, H. Jane; Lozano-Durán, Adrián; McKeon, Beverley

doi:10.1017/jfm.2020.857

Cited by 21 publications

(22 citation statements)

References 82 publications

(139 reference statements)

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“…Additionally, the azimuthal or oblique vortex, which seems to be the precursor of a streamwise vortex, is located between a HSS and a LSS. This configuration supports and gives further physical insight into the flow structures (sheared spanwise vortices located between oblique alternating streaks), which, through nonlinear interactions, form the dominant forcing mode associated with streamwise vortex regeneration (Bae et al 2021). The physical mechanisms responsible for the observed vortex autogeneration are further examined in § 5.…”

Section: Velocity Structuresmentioning

confidence: 52%

“…Similarly, recent particle image velocimetry results in TBL (Lee, Hutchis & Monty 2019) show that high-shear layers are formed due to the collision of large-scale structures travelling at different convection velocities. A very recent numerical study conducted on minimal channels at low and high Reynolds numbers by Bae et al (2021) revealed that when the most amplified nonlinear mode, identified through the use of resolvent analysis, is removed, the turbulence intensity in the buffer and logarithmic layers is significantly reduced. The same study determined by conditional averaging that the flow structures associated with the dominant nonlinear interactions of the SSP that regenerate streamwise vortices are sheared-spanwise vortical structures and oblique alternating streaks.…”

Section: Near-wall Organisation and Turbulence Self-sustaining Mechanismsmentioning

confidence: 99%

“…Since vorticity is not generated within the interior of the fluid (i.e. it is generated at the flow boundaries) (Batchelor 1967;Morton 1984), it is also natural to ask which mechanisms induce a vorticity intensification in the shear layer located between the high-and low-momentum structures, so that a vortex tube appears spontaneously. If there is a series of autogenerations due to the interactions of the LSMs after a BF event is identified, it would be insightful to determine the average time between autogenerations and how many BF events can autogenerate on the same LSS.…”

Section: Streak Collision and Breakdown Processmentioning

confidence: 99%

“…Understanding the near-wall region (y + 100) of wall-bounded turbulent flows has progressed substantially during the last century in several aspects, such as its statistical universality, organisation and self-sustaining mechanisms. Nevertheless, the nonlinearities that sustain near-wall turbulence still require a more profound understanding (McKeon 2017;Bae, Lozano-Durán & McKeon 2021) especially for unconstrained flows at high Reynolds numbers (Panton 2001). In that context, the present paper examines the precursors of rare backflow (BF) events and shows that these rare events are related to a nonlinear vortex autogeneration occurring near the wall.…”

Section: Introductionmentioning

confidence: 97%

“…This shows how dynamic and intermittent the near-wall region is. Additionally, essential turbulence quantities of canonical wall-bounded flows (pipe flow, channel flow and zero pressure gradient (ZPG) turbulent boundary layer (TBL)) such as vorticity (ω) are generated at the wall (Batchelor 1967;Morton 1984). Moreover, the large velocity gradients and the rate at which these quantities evolve near the wall significantly influence the intensification and dampening of vorticity within this region (Davidson 2004).…”

Section: Introductionmentioning

confidence: 99%

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Precursors of backflow events and their relationship with the near-wall self-sustaining process

2021

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This study examines the precursors and consequences of rare backflow events at the wall using direct numerical simulation of turbulent pipe flow with a high spatiotemporal resolution. The results obtained from conditionally averaged fields reveal that the precursor of a backflow event is the asymmetric collision between a high- and a low-speed streak (LSS) associated with the sinuous mode of the streaks. As the collision occurs, a lifted shear layer with high local azimuthal enstrophy is formed at the trailing end of the LSS. Subsequently, a spanwise or an oblique vortex spontaneously arises. The dominant nonlinear mechanism by which this vortex is engendered is enstrophy intensification due to direct stretching of the lifted vorticity lines in the azimuthal direction. As time progresses, this vortex tilts and orientates towards the streamwise direction and, as its enstrophy increases, it induces the breakdown of the LSS located below it. Subsequently, this vortical structure advects as a quasi-streamwise vortex, as it tilts and stretches with time. As a result, it is shown that reverse flow events at the wall are the signature of the nonlinear mechanism of the self-sustaining process occurring at the near-wall region. Additionally, each backflow event has been tracked in space and time, showing that approximately 50 % of these events are followed by at least one additional vortex generation that gives rise to new backflow events. It is also found that up to a maximum of seven regenerations occur after a backflow event has appeared for the first time.

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Section: Velocity Structuresmentioning

confidence: 52%

Section: Near-wall Organisation and Turbulence Self-sustaining Mechanismsmentioning

confidence: 99%

Section: Streak Collision and Breakdown Processmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

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Precursors of backflow events and their relationship with the near-wall self-sustaining process

2021

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The state space and travelling-wave solutions in two-scale wall-bounded turbulence

et al. 2022

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The computation of invariant solutions and the visualisation of the associated state space have played a key role in the understanding of transition and the self-sustaining process in wall-bounded shear flows. In this study, an extension of this approach is sought for a turbulent flow which explicitly exhibits multi-scale behaviour. The minimal unit of multi-scale near-wall turbulence, which resolves two adjacent spanwise integral length scales of motion, is considered using a shear stress-driven flow model (Doohan, Willis & Hwang J. Fluid Mech., vol. 913, 2021, A8). The edge state, 26 travelling waves and two periodic orbits are computed, which represent either the large- or small-scale self-sustaining processes. Given that the spanwise length scales are not widely separated here, it could be envisaged that turbulent trajectories visit these solutions in the state space. Considering the intra- and inter-scale dynamics of the flow, numerous phase portraits are examined, but the turbulent state is not found to approach any of these solutions. A detailed analysis reveals that this is due to the lack of scale interaction processes captured by the invariant solutions, including the mean–fluctuation interaction, the energy cascade in the streamwise wavenumber space and the cascade-driven energy production discovered recently. There is a single solution that resembles turbulence much more than the others, which captures two-scale energetics and a scale interaction process involving energy feeding from small to large spanwise scales through the subharmonic sinuous streak instability mode. Based on these observations, it is conjectured that the state space view of turbulent trajectories wandering between solutions would need suitable refinement to model multi-scale turbulence, when each solution does not represent multi-scale processes of turbulence. In particular, invariant solutions that are inherently multi-scale would be required.

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Interpolatory input and output projections for flow control

Herrmann,

Baddoo,

Dawson

et al. 2023

J. Fluid Mech.

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Eigenvectors of the observability and controllability Gramians represent responsive and receptive flow structures that enjoy a well-established connection to resolvent forcing and response modes. However, whereas resolvent modes have demonstrated great potential to guide sensor and actuator placement, observability and controllability modes have been leveraged exclusively in the context of model reduction via input and output projections. In this work, we introduce interpolatory, rather than orthogonal, input and output projections, that can be leveraged for sensor and actuator placement and open-loop control design. An interpolatory projector is an oblique projector with the property of preserving certain entries in the vector being projected. We review the connection between the resolvent operator and the Gramians, and present several numerical examples where we perform both orthogonal and interpolatory input and output projections onto the dominant forcing and response subspaces. Input projections are used to identify dynamically relevant disturbances, place sensors to measure disturbances, and place actuators for feedforward control in the linearized Ginzburg–Landau equation. Output projections are used to identify coherent structures and place sensors aiming at state reconstruction in the turbulent flow in a minimal channel at $Re_{\tau }=185$ . The framework does not require data snapshots and relies only on knowledge of the steady or mean flow.

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Nonlinear mechanism of the self-sustaining process in the buffer and logarithmic layer of wall-bounded flows

Abstract: Abstract

Cited by 21 publications

References 82 publications

Precursors of backflow events and their relationship with the near-wall self-sustaining process

Precursors of backflow events and their relationship with the near-wall self-sustaining process

The state space and travelling-wave solutions in two-scale wall-bounded turbulence

Interpolatory input and output projections for flow control

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