Three-dimensional optimal perturbations in viscous shear flow

Butler, Kathryn M.; Farrell, Brian F.

doi:10.1063/1.858386

Cited by 973 publications

(907 citation statements)

References 33 publications

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“…Ozdemir, Hsu & Balachandar (2014) have performed direct numerical simulations, and they confirm the observation of turbulent flows for Reynolds numbers above Re T = 900. A subcritical transition to turbulence is typical for wall-bounded shear flows, since this property is related to the non-normal nature of the linearised Navier-Stokes equations (Farrell 1988;Butler & Farrell 1992;Trefethen et al 1993;Schmid & Henningson 1999;Schmid 2007). Consequently, the idealised analytical flow has quite different stability properties from those seen in practice.…”

Section: Introductionmentioning

confidence: 99%

Transient growth of perturbations in Stokes oscillatory flows

Biau

2016

J. Fluid Mech.

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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. Oscillatory Stokes flows, with zero mean, are subjected to subcritical transition to turbulence. The maximal energy growth of perturbations is computed in the subcritical regime through an optimisation method. The results show strong amplifications during half a period. The energy transfer from the base flow involves an Orr mechanism with two-dimensional vorticity waves, and the maximum energy scales exponentially with the Reynolds number. Nonlinear simulations show that low-energy perturbations are sufficient to trigger turbulent flow.

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Section: Introductionmentioning

confidence: 99%

Transient growth of perturbations in Stokes oscillatory flows

Biau

2016

J. Fluid Mech.

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“…A vast amount of litterature has described the linear mechanisms responsible for disturbance amplification. Optimisation methods have yielded linear optimal disturbances [1,2], the disturbances which exhibit the largest linear growth. Yet the focus has been on linear amplification rather than on actual transition, which requires full nonlinearity to be taken into account.…”

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confidence: 99%

“…The minimal energy required by the simplest possible initial conditions approaching these is also compiled in the table. Edge II is reached by initial conditions consisting of streamwise rolls and a small amount of perturbation in the Fourier component (1,2), of the order of few percents of the total energy. Conversely, the solution denoted by III is approached by a perturbation where the energy in the oblique mode (1, 1) is about half of that of the streamwise rolls.…”

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confidence: 99%

Nonlinear optimal perturbations in plane Couette flow

Brandt¹,

Duguet²,

Larsson³

2009

Springer Proceedings in Physics

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Subcritical transition to turbulence can occur in a variety of wall-bounded shear flows when the laminar base state is not subject to linear instability. In this case, perturbations to the base state with a finite but very small amplitude can be amplified by non-normal effects, up to a level where nonlinear interactions come into play. Since transition is often undesired, leading to a dramatic increase in wall drag, it is important to know which kind of (weak) perturbations are susceptible to trigger it if we wish to delay it. A vast amount of litterature has described the linear mechanisms responsible for disturbance amplification. Optimisation methods have yielded linear optimal disturbances[1, 2], the disturbances which exhibit the largest linear growth. Yet the focus has been on linear amplification rather than on actual transition, which requires full nonlinearity to be taken into account. In this study, we go back to the original question of which perturbation is most likely to trigger transition to turbulence. We are hence investigating nonlinear optimal disturbances, those with smallest initial energy which effectively lead to a highly disordered flow. In the recent years, progress in the understanding of subcritical transition was made using the concept of 'edge states', originating from dynamical systems theory. 'Edge state' refers to the flow regime reached asymptotically by critical trajectories at the exact onset of transition. It is an unstable flow state and cannot be observed in experiments, but its stable manifold determines the basin of attraction of the base state. Direct numerical simulation in minimal domains of plane Couette flow has shown that the flow at the onset of transition asymptotically approaches an unstable finite-amplitude steady state solution, characterised by wavy streaks and streamwise rolls [3]. Using a shooting method, approach to such steady states is the way to characterise whether a transitional trajectory in phase space is actually an 'edge' trajectory.In our investigation, we also focus on plane Couette flow in a computational box of size 4πh × 2h × 2πh. The Reynolds number (based on the half-gap h) used for most of the computations presented here is 400. The numerical simulations are performed with a pseudospectral code using 48×33×48 grid points in

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“…During the last twenty years many dozens of papers about such growth were published (papers [14][15][16][17][18][19][20] represent only a few examples of them), while much attention to this topic was also given in books [21,22] and a survey [23]. It was shown, in particular, that transient growth of nonmodal disturbances may exceed very much the growth of the linearly unstable wave modes.…”

Section: Flow Instability and Transition To Turbulencementioning

confidence: 99%

“…It was shown, in particular, that transient growth of nonmodal disturbances may exceed very much the growth of the linearly unstable wave modes. This circumstance gave rise to keen interest to 'optimal disturbances' undergoing most intensive transient growth in a given laminar flow; see, e.g., papers [15,24,25] devoted to this subject. Note also that in the case of 'subcritical fluid flow' with Re <Re cr all solutions of linearized disturbance equations tend to zero as t ->°°.…”

Section: Flow Instability and Transition To Turbulencementioning

confidence: 99%

The Century of Turbulence Theory: The Main Achievements and Unsolved Problems

Yaglom¹

Les Houches - Ecole D’Ete De Physique Theorique

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Three-dimensional optimal perturbations in viscous shear flow

Cited by 973 publications

References 33 publications

Transient growth of perturbations in Stokes oscillatory flows

Transient growth of perturbations in Stokes oscillatory flows

Nonlinear optimal perturbations in plane Couette flow

The Century of Turbulence Theory: The Main Achievements and Unsolved Problems

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