Local and Global Instabilities in Spatially Developing Flows

Huerre, Patrick; Monkewitz, Peter A.

doi:10.1146/annurev.fl.22.010190.002353

Cited by 1,780 publications

(1,201 citation statements)

References 101 publications

(114 reference statements)

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“…Similar differences were apparent for the higher H cases and are not unexpected -it has been noted before that we only expect a global mode to appear in a real case if there is a sufficiently long axial region over which conditions for local absolute instability are satisfied (e.g. Hammond & Redekopp 1998;Huerre & Monkewitz 1990). In our NS computations, we cannot expect to identify the intermediate transition to local absolute instability; recall that Re cg denotes the point at which a self-sustained global mode first appears and that will occur only after a sufficiently large part of the flow has become absolutely unstable.…”

Section: Stability Calculations and Comparisonssupporting

confidence: 86%

The stability of laminar symmetric separated wakes

Castro

2005

J. Fluid Mech.

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Time-dependent computations of the two-dimensional incompressible uniformvelocity laminar flow past a normal flat plate (of unit half-width) in a channel are presented. Attention is restricted to cases in which the well-known anti-symmetric (von Kármán-type) vortex shedding is suppressed by the imposition of a symmetry plane on the downstream plate centreline. With a further symmetry plane at the channel's upper boundary, the only two governing parameters in the problem are the channel half-width, H , and the Reynolds number, Re (based on the body half-width and the upstream velocity, U ). The former is restricted to the range 3 6 H 6 30 and the interest lies in determining the nature of the initial instability which occurs in the separated wake as Re is gradually increased. It is found that for sufficiently large H and at a critical Re, a long-time-scale global (supercritical) instability is initiated, which in its saturated (limit) state takes the form of 'lumps' of vorticity being periodically shed from the tail end of the separated bubble. Stability calculations of corresponding mean flow profiles (typical of those found in the separated wake) are undertaken by examining the impulse response of particular profiles via appropriate solution of the Orr-Sommerfeld equation. The results of this analysis extend those available from related published work and are consistent with the behaviour found from the numerical computations. Taken together, all the results suggest that this type of global instability may be generic to many kinds of separated wakes and, indeed, may provide the fundamental explanation for the very low-frequency oscillations often noticed in fully turbulent wake bubbles.

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Section: Stability Calculations and Comparisonssupporting

confidence: 86%

The stability of laminar symmetric separated wakes

Castro

2005

J. Fluid Mech.

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“…In contrast, convective instabilities are characterised by a dominating advection of the perturbations and behave as amplifiers of the noise that may exist in the system. 9 In co-axial injection devices, an absolutely unstable configuration is expected to result in a self-sustained formation of droplets close to the device inlet, while a convectively unstable flow is expected to result in droplets which form a finite distance downstream, only after the instability has had space to grow.…”

Section: A Co-flowing Streamsmentioning

confidence: 99%

“…7 Moreover, small variations of the driving conditions can lead to transitions between the production of drops or of stable jets, a classical signature of nonlinear instabilities. 8,9 These transitions between widely different behaviours are possible because modifications in the drop geometry couple back to the flow profiles and amplify initially small variations.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of microfluidic droplets

2010

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This critical review discusses the current understanding of the formation, transport, and merging of drops in microfluidics. We focus on the physical ingredients which determine the flow of drops in microchannels and recall classical results of fluid dynamics which help explain the observed behaviour. We begin by introducing the main physical ingredients that differentiate droplet microfluidics from single-phase microfluidics, namely the modifications to the flow and pressure fields that are introduced by the presence of interfacial tension. Then three practical aspects are studied in detail: (i) The formation of drops and the dominant interactions depending on the geometry in which they are formed.(ii) The transport of drops, namely the evaluation of drop velocity, the pressure-velocity relationships, and the flow field induced by the presence of the drop. (iii) The fusion of two drops, including different methods of bridging the liquid film between them which enables their merging.

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“…Note that in both cases mentioned above, the shear layer is locally convectively unstable (i.e. not absolutely unstable), using the terminology of Huerre & Monkewitz (1990). However, the flow may still be globally unstable if the acoustic feedback provides a loop gain that is greater than unity.…”

Section: Experimental Dynamicsmentioning

confidence: 99%

Linear models for control of cavity flow oscillations

et al. 2006

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Models for understanding and controlling oscillations in the flow past a rectangular cavity are developed. These models may be used to guide control designs, to understand performance limits of feedback, and to interpret experimental results. Traditionally, cavity oscillations are assumed to be self-sustained: no external disturbances are necessary to maintain the oscillations, and amplitudes are limited by nonlinearities. We present experimental data which suggests that in some regimes, the oscillations may not be self-sustained, but lightly damped: oscillations are sustained by external forcing, such as boundary-layer turbulence. In these regimes, linear models suffice to describe the behaviour, and the final amplitude of oscillations depends on the characteristics of the external disturbances. These linear models are particularly appropriate for describing cavities in which feedback has been used for noise suppression, as the oscillations are small and nonlinearities are less likely to be important. It is shown that increasing the gain too much in such feedback control experiments can lead to a peak-splitting phenomenon, which is explained by the linear models. Fundamental performance limits indicate that peak splitting is likely to occur for narrow-bandwidth actuators and controllers.

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Local and Global Instabilities in Spatially Developing Flows

Cited by 1,780 publications

References 101 publications

The stability of laminar symmetric separated wakes

The stability of laminar symmetric separated wakes

Dynamics of microfluidic droplets

Linear models for control of cavity flow oscillations

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