Transition of streamwise streaks in 
zero-pressure-gradient boundary layers

Brandt, Luca; Henningson, Dan S.

doi:10.1017/s0022112002002331

Cited by 130 publications

(78 citation statements)

References 59 publications

(95 reference statements)

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“…The predicted critical amplitude compares more favourably with the previously cited experimental observations than the steady, inviscid results of Andersson et al (2001). For example, even the highest-amplitude streaks in the Brandt & Henningson (2002) asserted that the boundary layer had nearly equal propensity to undergo sinuous or varicose instability based on their DNS of bypass transition. This difference can be explained by the results of the unsteady analysis.…”

Section: The Influence Of Unsteady Base Flow On the Outer Modesupporting

confidence: 72%

“…They reported critical streak amplitudes of 26% and 37% for the sinuous and varicose instability modes, respectively. These modes were subsequently prescribed as inlet perturbations in the DNS of Brandt & Henningson (2002). The simulations affirmed the amplification of the secondary instability modes, which resulted in breakdown to turbulence.…”

Section: The Instability Due To Klebanoff Streaks In Bypass Transitionmentioning

confidence: 73%

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Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

2011

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The secondary instability of a zero-pressure-gradient boundary layer, distorted by unsteady Klebanoff streaks, is investigated. The base profiles for the analysis are computed using direct numerical simulation (DNS) of the boundary-layer response to forcing by individual free-stream modes, which are low frequency and dominated by streamwise vorticity. Therefore, the base profiles take into account the nonlinear development of the streaks and mean flow distortion, upstream of the location chosen for the stability analyses. The two most unstable modes were classified as an inner and an outer instability, with reference to the position of their respective critical layers inside the boundary layer. Their growth rates were reported for a range of frequencies and amplitudes of the base streaks. The inner mode has a connection to the TollmienSchlichting (T-S) wave in the limit of vanishing streak amplitude. It is stabilized by the mean flow distortion, but its growth rate is enhanced with increasing amplitude and frequency of the base streaks. The outer mode only exists in the presence of finite amplitude streaks. The analysis of the outer instability extends the results of Andersson et al. (J. Fluid Mech. vol. 428, 2001, p. 29) to unsteady base streaks. It is shown that base-flow unsteadiness promotes instability and, as a result, leads to a lower critical streak amplitude. The results of linear theory are complemented by DNS of the evolution of the inner and outer instabilities in a zero-pressure-gradient boundary layer. Both instabilities lead to breakdown to turbulence and, in the case of the inner mode, transition proceeds via the formation of wave packets with similar structure and wave speeds to those reported by Nagarajan, Lele & Ferziger (J. Fluid Mech., vol. 572, 2007, p. 471).

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Section: The Influence Of Unsteady Base Flow On the Outer Modesupporting

confidence: 72%

Section: The Instability Due To Klebanoff Streaks In Bypass Transitionmentioning

confidence: 73%

Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

2011

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“…In conclusion we observed a turbulence sustaining mechanism which has previously only been identified in numerical calculations and which is believed to be of relevance to transition [29] and energy regeneration in shear flows [14,25,28]. This mechanism was identified as part of a traveling wave transient in the turbulent flow.…”

Section: Fig 3 (Color Online)supporting

confidence: 62%

“…Similarly in a numerical study of turbulence in a minimal flow unit [27,28] a TW consisting of a wavy streak aligned by streamwise vortices was identified in a wall shear flow. Wavy streaks sandwiched between counterrotating streamwise vortices have also been observed by Brandt et al [29] during the transition process in boundary layers.…”

supporting

confidence: 64%

Turbulence Regeneration in Pipe Flow at Moderate Reynolds Numbers

et al. 2005

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We present the results of an experimental investigation into the nature and structure of turbulent pipe flow at moderate Reynolds numbers. A turbulence regeneration mechanism is identified which sustains a symmetric traveling wave within the flow. The periodicity of the mechanism allows comparison to the wavelength of numerically observed exact traveling wave solutions and close agreement is found. The advection speed of the upstream turbulence laminar interface in the experimental flow is observed to form a lower bound on the phase velocities of the exact traveling wave solutions. Overall our observations suggest that the dynamics of the turbulent flow at moderate Reynolds numbers are governed by unstable nonlinear traveling waves. A process which is believed to be of relevance for transition in shear flows is the so called lift-up mechanism [6]. Here streamwise vortices of relatively small magnitude transport low momentum fluid away from the wall and high momentum fluid towards the wall creating strong anomalies in the velocity profile, so-called low-and high-speed streaks (elongated regions of low or high streamwise velocity with respect to their surroundings). During this process the initial perturbation amplitude can grow substantially. Since the mechanism is of a linear nature, in linearly stable flows eventually all perturbations will decay. However it is assumed that once the perturbation has reached a sufficiently large amplitude nonlinear effects will become important and lead to secondary instabilities. The mathematical reason for the transient growth of initial perturbations is the non-normality of the linearized NavierStokes operator and this mechanism has attracted considerable attention [7][8][9].In more recent studies the relevance of nonlinear effects and, in particular, the role of nonlinear solutions has been discussed [10,11]. Such solutions have been calculated for Couette and Poiseuille flow [12 -16] and more recently also for pipe flow [17,18]. These new flow states arise at finite values of the control parameter (Re) and in the case of pipe flow they take the form of traveling waves (TWs), which are coherent flow structures propagating at a constant phase speed in the streamwise direction. Typically these TW solutions are unstable so that the laminar flow state remains the only stable solution. In analogy to observations in low dimensional models [19,20] it has been suggested that as the Reynolds number is increased further the unstable states undergo secondary bifurcations and form an attracting region in phase space which gives rise to turbulent dynamics. The basin of attraction of the turbulent state grows with increasing Reynolds number, so that smaller and smaller perturbations are sufficient to destabilize the laminar flow.Confirmation of this picture has been provided by recent experiments in pipe flow where transients of unstable TWs have been observed that are in close agreement with the numerical solutions [21]. Further experimental investigations have demonstrated that the sta...

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“…Brandt & Henningson 2002;Zaki & Durbin 2005;Schlatter et al 2008;Mandal, Venkatakrishnan & Dey 2010;Nolan, Walsh & Mceligot 2010;Nolan & Walsh 2012). Additionally, Andersson et al (2001), Vaughan & Zaki (2011) and Hack & Zaki (2014) have performed secondary instability analysis of streaks.…”

Section: Bypass Transitionmentioning

confidence: 99%

Transition of transient channel flow after a change in Reynolds number

Seddighi

2015

J. Fluid Mech.

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It has previously been shown that the transient flow in a channel following a step increase of Reynolds number from 2800 to 7400 (based on channel half-height and bulk velocity) is effectively a laminar-turbulent bypass transition even though the initial flow is turbulent (He & Seddighi, J. Fluid Mech., vol. 715, 2013, pp. 60-102). In this paper, it is shown that the transient flow structures exhibit strong contrasting characteristics in large and small flow perturbation scenarios. When the increase of Reynolds number is large, the flow is characterized by strong elongated streaks during the initial period, followed by the occurrence and spreading of isolated turbulent spots, as shown before. By contrast, the flow appears to evolve progressively and the turbulence regeneration process remains largely unchanged during the flow transient when the Reynolds number ratio is low, and streaks do not appear to play a significant role. Despite the major apparent differences in flow structures, the transient flow under all conditions considered is unambiguously characterized by laminar-turbulent transition, which exhibits itself clearly in various flow statistics. During the pre-transition period, the time-developing boundary layers in all the cases show a strong similarity to each other and follow closely the Stokes solution for a transient laminar boundary layer. The streamwise fluctuating velocity also shows good similarity in the various cases, irrespective of the appearance of elongated streaks or not, and the maximum energy growth exhibits a linear rate similar to that in a spatially developing boundary layer. The onset of transition is clearly definable in all cases using the minimum friction factor, and the critical time thus defined is strongly correlated with the free-stream turbulence in a power-law form.

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Transition of streamwise streaks in zero-pressure-gradient boundary layers

Cited by 130 publications

References 59 publications

Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

Stability of zero-pressure-gradient boundary layer distorted by unsteady Klebanoff streaks

Turbulence Regeneration in Pipe Flow at Moderate Reynolds Numbers

Transition of transient channel flow after a change in Reynolds number

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