Theory and Computation in Hydrodynamic Stability

Criminale, W. O.; Jackson, T. L.; Joslin, Ronald D.

doi:10.1017/9781108566834

Cited by 33 publications

(42 citation statements)

References 345 publications

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“…In a general turbulent flow, fluctuations are stationary random functions, which can be meaningfully characterised either via single-point statistics such as the mean, the variance or the autocorrelation function; or in terms of twopoint statistics, via the cross-correlation function. In the frequency domain, the most complete description of two-point statistics is provided by the cross-spectral density function, which is the Fourier transform of the cross-correlation function [56], but can also be defined as the expected value, P qq = E(qq H ), (24) where q here denotes a Fourier transform taken for a given realisation, and E is the expected-value operator, which amounts to an average of several realisations. Once q is discretised, P qq becomes a cross-spectral-density matrix, which is Hermitian; its main diagonal contains the real, positive power spectral densities (PSDs) of flow quantities at given spatial locations.…”

Section: Response To Stochastic Forcing 241 Frequency-domain Statismentioning

confidence: 99%

“…The possibility of using linear stability theory to model turbulence dynamics is clearly attractive. Due to the interest in laminar-turbulent transition, a substantial body of knowledge exists and has been compiled in monographs [23,24] and review articles [25,26,27]. Linearisation of the flow equations simplifies most of the numerical work, and, perhaps more importantly, leads to a clearer understanding of relevant flow mechanisms, which become analogous to phenomena seen in transition: the growth of structures near the nozzle can, for instance, be associated with the equivalent Kelvin-Helmholtz instability observed in transitional flows.…”

Section: Introductionmentioning

confidence: 99%

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Wave-Packet Models for Jet Dynamics and Sound Radiation

Cavalieri

Jordan

Lesshafft

2019

Applied Mechanics Reviews

107

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Organized structures in turbulent jets can be modeled as wavepackets. These are characterized by spatial amplification and decay, both of which are related to stability mechanisms, and they are coherent over several jet diameters, thereby constituting a noncompact acoustic source that produces a distinctive directivity in the acoustic field. In this review, we use simplified model problems to discuss the salient features of turbulent-jet wavepackets and their modeling frameworks. Two classes of model are considered. The first, that we refer to as kinematic, is based on Lighthill's acoustic analogy, and allows an evaluation of the radiation properties of sound-source functions postulated following observation of jets. The second, referred to as dynamic, is based on the linearized, inhomogeneous Ginzburg–Landau equation, which we use as a surrogate for the linearized, inhomogeneous Navier–Stokes system. Both models are elaborated in the framework of resolvent analysis, which allows the dynamics to be viewed in terms of an input–ouput system, the input being either sound-source or nonlinear forcing term, and the output, correspondingly, either farfield acoustic pressure fluctuations or nearfield flow fluctuations. Emphasis is placed on the extension of resolvent analysis to stochastic systems, which allows for the treatment of wavepacket jitter, a feature known to be relevant for subsonic jet noise. Despite the simplicity of the models, they are found to qualitatively reproduce many of the features of turbulent jets observed in experiment and simulation. Sample scripts are provided and allow calculation of most of the presented results.

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Section: Response To Stochastic Forcing 241 Frequency-domain Statismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Wave-Packet Models for Jet Dynamics and Sound Radiation

Cavalieri

Jordan

Lesshafft

2019

Applied Mechanics Reviews

107

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“…By taking appropriate linear combinations of ̂( 0) and ̂ 2, two families of solutions can be formed that are distinguished by the value of ̂ at = 0. Specifically, "even" and "odd" modes can be identified such that for the even mode ̂≠ 0 at = 0, while for the odd mode In this investigation, however, only the even mode is considered, primarily because very many related stability problems the even mode is known to be the fastest-growing mode [34] .…”

Section: Appendixmentioning

confidence: 99%

Shear instability of plastically-deforming metals in high-velocity impact welding

Nassiri

Kinsey

Chini

2016

Journal of the Mechanics and Physics of Solids

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High-speed oblique impact of two metal plates results in the development of an intense shear region at their interface leading to interfacial profile distortion and interatomic bonding. If the relative velocity is sufficient, a distinct wavy morphology with a well-defined amplitude and wavelength is observed. Emergence of this morphology below the melting point of the metal plates is usually taken as evidence of a successful weld. Among various proposed mechanisms, instability owing to large tangential velocity variations near the interface has received significant attention. With one exception, the few quantitative stability analyses of this proposed mechanism have treated an anti-symmetric/shear-layer base profile (i.e., a Kelvin-Helmholtz configuration) and employed an inviscid or Newtonian viscous fluid constitutive relation. The former stipulation implies the energy source for the instability is the presumed relative shearing motion of the two plates, while the latter is appropriate only if melting occurs locally near the interface. In this study, these restrictions, which are at odds with the conditions realized in high-velocity impact welding, are relaxed. A quantitative temporal linear stability analysis is performed to investigate whether the interfacial wave morphology could be the signature of a shear-driven high strain-rate instability of a perfectly plastic material undergoing a jet-like deformation near the interface. The resulting partial differential eigenvalue problem is solved numerically using a spectral collocation method in which customized boundary conditions near the interface are implemented to properly treat the singularity arising from the vanishing of the base flow strain-rate at the symmetry plane of the jet. The solution of the eigenvalue problem yields the wavelength and growth rate of the dominant wave-like

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“…Напомним, что в соответствии с существующим представлением об устойчивости плоских течений наличие точки перегиба : 2 2 ( ) = 0 профиля скорости ( ) является необходимым условием возникновения неустойчивости при пренебрежимо малой вязкости (так называемый механизм возникновения «невязкой неустойчивости»). При этом в случае нейтральной устойчивости (Re = Re L ) точка перегиба должна совпадать с «критической» точкой , в которой скорость основного течения равна фазовой скорости ведущей моды: ( ) = [59]. Это позволяет объяснить зависимость устойчивости основного течения от профиля его скорости и предсказать области наибольших значений модуля продольной компоненты скорости ведущей моды, то есть области возникновения и развития неустойчивости.…”

Section: линейное критическое число рейнольдсаunclassified

Stability of shear flows over a grooved surface

Бойко¹,

Klyushnev²,

Nechepurenko³

2016

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Theory and Computation in Hydrodynamic Stability

Cited by 33 publications

References 345 publications

Wave-Packet Models for Jet Dynamics and Sound Radiation

Wave-Packet Models for Jet Dynamics and Sound Radiation

Shear instability of plastically-deforming metals in high-velocity impact welding

Stability of shear flows over a grooved surface

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