Self-Sustained Localized Structures in a Boundary-Layer Flow

Duguet, Yohann; Schlatter, Philipp; Henningson, Dan S.; Eckhardt, Bruno

doi:10.1103/physrevlett.108.044501

Cited by 62 publications

(88 citation statements)

References 22 publications

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“…Efforts to develop a similar dynamical understanding of transition in extended flows have lead to the computation of a number of localized edge states, but to date these have either been invariant states localized in a single homogeneous direction (Schneider et al 2010b;Avila et al 2013;Khapko et al 2013;Zammert & Eckhardt 2014) or doubly-localized but chaotically wandering states without well-defined stable and unstable manifolds (Schneider et al 2010b;Duguet et al 2012). The doubly-localized invariant solution in this paper thus provides a potential starting point for addressing spatiotemporal transition of extended flows in dynamical terms.…”

Section: Stability and The Evolution Of Unstable Perturbationsmentioning

confidence: 99%

A doubly localized equilibrium solution of plane Couette flow

Brand

Gibson

2014

J. Fluid Mech.

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We present an equilibrium solution of plane Couette flow that is exponentially localized in both the spanwise and streamwise directions. The solution is similar in size and structure to previously computed turbulent spots and localized, chaotically wandering edge states of plane Couette flow. A linear analysis of dominant terms in the Navier-Stokes equations shows how the exponential decay rate and the wall-normal overhang profile of the streamwise tails are governed by the Reynolds number and the dominant spanwise wavenumber. Perturbations of the solution along its leading eigenfunctions cause rapid disruption of the interior roll-streak structure and formation of a turbulent spot, whose growth or decay depends on the Reynolds number and the choice of perturbation.

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Section: Stability and The Evolution Of Unstable Perturbationsmentioning

confidence: 99%

A doubly localized equilibrium solution of plane Couette flow

Brand

Gibson

2014

J. Fluid Mech.

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“…The dynamical system theory of transition that has been promoted by these authors, among others, relies on the idea that transition and turbulence can be explained as a walk of the system's state among exact coherent states, which are unstable fixed points, periodic orbits or chaotic solutions of the Navier-Stokes equations. Some of these solutions, called edge states, live in the phase-space on the boundary between the laminar and the turbulent attractors, acting as relative attractors for the states evolving along its stable manifold (Skufca et al (2006);Schneider et al (2007); Cherubini et al (2011a); Duguet et al (2012)). The perturbations living on the laminar-turbulent boundary are very interesting since they can be the most dangerous, being the closest ones to the laminar state capable to trigger transition.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow

2013

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. 1Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow The present work provides an optimal control strategy, based on the nonlinear NavierStokes equations, aiming at hampering the rapid growth of unsteady finite-amplitude perturbations in a Blasius boundary-layer flow. A variational procedure is used to find the blowing and suction control law at the wall providing the maximum damping of the energy of a given perturbation at a given target time, with the final aim of leading the flow back to the laminar state. Two optimally-growing finite-amplitude initial perturbations capable of leading very rapidly to transition have been used to initialize the flow. The nonlinear control procedure has been found able to drive such perturbations back to the laminar state, provided that the target time of the minimisation and the region in which the blowing and suction is applied have been suitably chosen. On the other hand, an equivalent control procedure based on the linearized Navier-Stokes equations has been found much less effective, being not able to lead the flow to the laminar state when finite-amplitude disturbances are considered. Regions of strong sensitivity to blowing and suction have been also identified for the given initial perturbations: when the control is actuated in such regions, laminarization is observed also for a shorter extent of the actuation region. The nonlinear optimal blowing and suction law consists of alternated wall-normal velocity perturbations, which appear to modify the core flow structures by means of two distinct mechanisms: i) a wall-normal velocity-compensation at small times; ii) a rotationcounterbalancing effect al larger times. Similar control laws have been observed for different target times, values of the cost parameter, and streamwise extents of the blowing and suction zone, meaning that these two mechanisms are robust features of the optimal control strategy, provided that the nonlinear effects are taken into account.

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“…We see the main feature of the transitional regimes -localized turbulent spots with laminar flow between them. Localized turbulent spots are well known from HD wall-bounded shear flows [22][23][24][25][26][27] and can be considered in the broader context of patterned turbulence. The best known example is pipe flow, where the spots are known since [9].…”

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confidence: 99%