Optimal perturbations and streak spacing in wall-bounded turbulent shear flow

Butler, Kathryn M.; Farrell, Brian F.

doi:10.1063/1.858663

Cited by 205 publications

(249 citation statements)

References 9 publications

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“…Of particular importance has been the recognition that linear mechanisms play a key role in controlling the transition to turbulence at low Reynolds number (Trefethen et al 1993;Henningson & Reddy 1994), as well as generating and sustaining the dynamically important coherent structures that characterize wall turbulence (e.g. Butler & Farrell 1993;Schoppa & Hussain 2002;Kim 2011). As a result, the application of concepts from control theory has led to the design of many successful control strategies that delay the onset of turbulence (Joshi, Speyer & Kim 1997), relaminarize turbulent flows (Högberg, Bewley & Henningson 2003;Sharma et al 2011), or reduce turbulent kinetic energy (Lim & Kim 2004).…”

Section: Feedback Flow Controlmentioning

confidence: 99%

Opposition control within the resolvent analysis framework

2014

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as an example. Under this formulation, the velocity field for turbulent pipe flow is decomposed into a series of highly amplified (rank-1) response modes, identified from a gain analysis of the Fourier-transformed NavierStokes equations. These rank-1 velocity responses represent propagating structures of given streamwise/spanwise wavelength and temporal frequency, whose wall-normal footprint depends on the phase speed of the mode. Opposition control, introduced via the boundary condition on wall-normal velocity, affects the amplification characteristics (and wall-normal structure) of these response modes; a decrease in gain indicates mode suppression, which leads to a decrease in the drag contribution from that mode. With basic assumptions, this rank-1 model reproduces trends observed in previous direct numerical simulation and large eddy simulation, without requiring high-performance computing facilities. Further, a wavenumber-frequency breakdown of control explains the deterioration of opposition control performance with increasing sensor elevation and Reynolds number. It is shown that slower-moving modes localized near the wall (i.e. attached modes) are suppressed by opposition control. Faster-moving detached modes, which are more energetic at higher Reynolds number and more likely to be detected by sensors far from the wall, are further amplified. These faster-moving modes require a phase lag between sensor and actuator velocity for suppression. Thus, the effectiveness of opposition control is determined by a trade-off between the modes detected by the sensor. However, it may be possible to develop control strategies optimized for individual modes. A brief exploration of such mode-optimized control suggests the potential for significant performance improvement.

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Section: Feedback Flow Controlmentioning

confidence: 99%

Opposition control within the resolvent analysis framework

2014

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“…The importance of this nondimensional interval was recognized by Lee et al (1990) who provide estimates which are shown in Figure 4. Butler and Farrell (1993) showed that the perturbations in the turbulent sublayer that optimize energy in an eddy turnover time characteristic of sublayer turbulence have the observed z + = 100 streak spacing.…”

Section: D the Role Of Finite Coherence Time In Shear Turbulencementioning

confidence: 99%

“…This result implies that streaks arise naturally from small random disturbances and explains the ubiquity of streaks in shear flow. The mechanism responsible for selecting the z + ≈ 100 spanwise spacing of the sublayer streaks was subsequently clarified by Butler and Farrell (1993). Their results were obtained making use of optimal perturbation theory which provides a constructive method for finding the perturbation with the greatest increase in energy over a specified interval of time (B&F).…”

Section: Introductionmentioning

confidence: 99%

“…In this work the parameterization of finite time disruption exploited in Butler and Farrell, (1993) and Farrell and Ioannou (1993a) to obtain the coherent structures in the boundary layer is extended to obtain the boundary-layer-frequency/wave-number spectra of Morrison and Kronauer (1969). To this purpose a method of accounting for the finite time correlation of disturbances in stochastically forced boundary layer flow is developed and the success of the resulting simulation of boundary layer turbulence provides support for a mechanistic theory of turbulence based on the properties of the highly nonnormal dynamical operator arising in strong shear.…”

Section: Introductionmentioning

confidence: 99%

“…Their results were obtained making use of optimal perturbation theory which provides a constructive method for finding the perturbation with the greatest increase in energy over a specified interval of time (B&F). The essential additional physically based parameter used by Butler and Farrell (1993) is this interval of time which is chosen to be the decorrelation time in the flow as estimated from the observed eddy turnover time. Using this parametrization the observed streak structure is found to correspond closely with the most amplified perturbation when the appropriate Reynolds-Tiederman boundary layer profile is taken.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Perturbation Structure and Spectra in Turbulent Channel Flow

Farrell

Ioannou

1998

Theoretical and Computational Fluid Dynamics

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Abstract. The strong mean shear in the vicinity of the boundaries in turbulent boundary layer flows preferentially amplifies a particular class of perturbations resulting in the appearance of coherent structures and in characteristic associated spatial and temporal velocity spectra. This enhanced response to certain perturbations can be traced to the nonnormality of the linearized dynamical operator through which transient growth arising in dynamical systems with asymptotically stable operators is expressed. This dynamical amplification process can be comprehensively probed by forcing the linearized operator associated with the boundary layer flow stochastically to obtain the statistically stationary response.In this work the spatial wave-number/temporal frequency spectra obtained by stochastically forcing the linearized model boundary layer operator associated with wall-bounded shear flow at large Reynolds number are compared with observations of boundary layer turbulence. The verisimilitude of the stochastically excited synthetic turbulence supports the identification of the underlying dynamics maintaining the turbulence with nonnormal perturbation growth.

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Hydrodynamic Stability and Turbulence: Beyond Transients to a Self‐Sustaining Process

1995

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Transition from laminar to turbulent flows has generally been studied by considering the linear and weakly nonlinear evolution of small disturbances to the laminar flow. That approach has been fruitless for many shear flows, and a last hope for its success has been the existence of transient growth phenomena. The physical origin of those linear transient effects is elucidated, revealing serious limitations both of previous analyses and of the phenomena themselves, which preclude them from causing direct transition. Nonetheless, some transient effects are symptomatic of one element of a nonlinear process that becomes self-sustaining at a small enough dissipation. The process is identified, and its description requires a departure from the traditional focus on the laminar flow. A theory is outlined in which the mean flow has an intrinsic span wise variation. Evidence indicates this is also the central mechanism in the near wall-region of fully turbulent shear flows.

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Optimal perturbations and streak spacing in wall-bounded turbulent shear flow

Cited by 205 publications

References 9 publications

Opposition control within the resolvent analysis framework

Opposition control within the resolvent analysis framework

Perturbation Structure and Spectra in Turbulent Channel Flow

Hydrodynamic Stability and Turbulence: Beyond Transients to a Self‐Sustaining Process

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