On the origin of streamwise vortices in a turbulent boundary layer

Jang, Pong Soo; Benney, D. J.; Gran, R. L.

doi:10.1017/s0022112086000551

Cited by 72 publications

(46 citation statements)

References 19 publications

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“…Indeed, localized streamwise roll and streak initial conditions are observed to decay in the presence of very low FST (Alfredsson & Matsubara 1996;Bakchinov et al 1997;Westin et al 1998). An alternative, and potentially complementary, mechanism is the formation of streamwise rolls and streaks from the nonlinear interaction of oblique waves (Benney 1960(Benney , 1984Jang et al 1986; Because this system is stable at every instance of time, it would asymptotically approach the zero perturbation state if its mean state time dependence were suppressed. This figure implies that the non-normal parametric mechanism maintains perturbation variance in both these self-sustaining states: (a) R = 800, σ r < 0.16, σ r = 0.045; (b) R = 800, σ r < −0.001, σ r = −0.0011.…”

Section: Discussionmentioning

confidence: 99%

“…The nonlinear non-normal mechanism can result from streamwise roll forcing by interacting discrete oblique waves and/or Tollmien-Schlichting waves (Benney 1960(Benney , 1984Jang, Benney & Gran 1986;Schmid & Henningson 1992;Reddy et al 1998;Brandt, Henningson & Ponziani 2002) and from Reynolds stresses associated with marginally stable critical layers (Hall & Sherwin 2010).…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow

2012

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Streamwise rolls and accompanying streamwise streaks are ubiquitous in wall-bounded shear flows, both in natural settings, such as the atmospheric boundary layer, as well as in controlled settings, such as laboratory experiments and numerical simulations. The streamwise roll and streak structure has been associated with both transition from the laminar to the turbulent state and with maintenance of the turbulent state. This close association of the streamwise roll and streak structure with the transition to and maintenance of turbulence in wall-bounded shear flow has engendered intense theoretical interest in the dynamics of this structure. In this work, stochastic structural stability theory (SSST) is applied to the problem of understanding the dynamics of the streamwise roll and streak structure. The method of analysis used in SSST comprises a stochastic turbulence model (STM) for the dynamics of perturbations from the streamwise-averaged flow coupled to the associated streamwise-averaged flow dynamics. The result is an autonomous, deterministic, nonlinear dynamical system for evolving a second-order statistical mean approximation of the turbulent state. SSST analysis reveals a robust interaction between streamwise roll and streak structures and turbulent perturbations in which the perturbations are systematically organized through their interaction with the streak to produce Reynolds stresses that coherently force the associated streamwise roll structure. If a critical value of perturbation turbulence intensity is exceeded, this feedback results in modal instability of the combined streamwise roll/streak and associated turbulence complex in the SSST system. In this instability, the perturbations producing the destabilizing Reynolds stresses are predicted by the STM to take the form of oblique structures, which is consistent with observations. In the SSST system this instability exists together with the transient growth process. These processes cooperate in determining the structure of growing streamwise roll and streak. For this reason, comparison of SSST predictions with experiments requires accounting for both the amplitude and structure of initial perturbations as well as the influence of the SSST instability. Over a range of supercritical turbulence intensities in Couette flow, this instability equilibrates to form finite amplitude time-independent streamwise roll and streak structures. At sufficiently high levels of forcing of the perturbation field, equilibration of the streamwise roll and streak structure does not occur and the flow transitions to a time-dependent state. This time-dependent state is self-sustaining in the sense that it persists when the forcing is removed. Moreover, this self-sustaining state rapidly evolves toward a minimal representation of wall-bounded shear flow turbulence in which the dynamics is limited to interaction of the streamwise-averaged flow with a perturbation structure at one † Email address for correspondence: pjioannou@phys.uoa.gr 150 B. F. Farrell and P. J. Ioannou st...

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow

2012

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“…[8][9][10] It has been shown 11 that the statistically dominant streamwise fluctuation exhibits wavelike characteristics, suggesting that a hydrodynamic wave description for the streamwise structures can be applicable. Models based on hydrodynamic stability theory for the coherent structures in both the outer and the near-wall regions of flat-plate boundary layers were reported.…”

Section: Introductionmentioning

confidence: 99%

“…Models based on hydrodynamic stability theory for the coherent structures in both the outer and the near-wall regions of flat-plate boundary layers were reported. 9,10 Jang et al 8 proposed a direct resonance theory to describe the bursting events. The structures are described as wavelike disturbances of the turbulent mean flow.…”

Section: Introductionmentioning

confidence: 99%

Bursting Frequency Predictions for Compressible Turbulent Boundary Layers

Liou

Fang

2003

AIAA Journal

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A computational method for the prediction of the bursting frequency associated with the coherent streamwise structures in high-speed compressible turbulent boundary layers is presented. The structures are described as wavelike disturbances of the turbulent mean flow. A direct resonance theory is used to determine the frequency of bursting. The resulting hydrodynamic linear stability equations are discretized by using a Chebyshev collocation method. A global numerical method capable of resolving the entire eigenvalue spectrum is used. Realistic turbulent mean velocity and temperature profiles are applied. For all of the compressible turbulent boundary layers calculated, the results show at least one frequency that satisfies the resonance condition. A second frequency can be identified for cases with high Reynolds numbers. An estimate is also made for the profile distribution of the temperature disturbance.

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“…Roll patterns appear as streaks in experiments [5]. Theoretical models for their existence have been offered [6,7], but no generally accepted theory exists. The remaining turbulent fiuctuations appear as propagating modes which travel downstream at a speed close to the mean speed at the locus of maximal Reynolds stress [4,8].…”

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confidence: 99%

Dynamical model of wall-bounded turbulence

Sirovich¹,

Zhou²

1994

Phys. Rev. Lett.

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Three complex ordinary differential equations, modeling interactions in wall-bounded turbulent flow, are developed and studied. It is believed that the roll-wave interactions which are included are of fundamental importance to turbulence production. Integration of these triad equations is shown to be consistent with direct flow simulations and the Ruelle-Takens route to chaos.PACS numbers: 47.27. -i Wall-bounded turbulent flow is characterized by a sequence of events in which a relatively slow moving wall fluid bursts [1] into the fast moving core fluid, and the fast moving core fluid stueeps [2] into the wall region (see also Ref. [3]). These events, which occur roughly 20% of

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On the origin of streamwise vortices in a turbulent boundary layer

Cited by 72 publications

References 19 publications

Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow

Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow

Bursting Frequency Predictions for Compressible Turbulent Boundary Layers

Dynamical model of wall-bounded turbulence

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