The Evolution of Linearized Perturbations of Parallel Flows

Criminale, W. O.; Drazin, P. G.

doi:10.1002/sapm1990832123

Cited by 98 publications

(65 citation statements)

References 13 publications

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“…The nearest solution we found is the velocity field given by Criminale & Drazin [21] for the initial value problem of an impulsive point source in a linear shear layer. Therefore, we will give the solution in detail.…”

Section: The Trailing Vorticity Field Behind a Point Source In Inmentioning

confidence: 87%

The critical layer in sheared flow

Darau

Rienstra

2011

17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference)

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Critical layers arise as a singularity of the linearized Euler equations when the phase speed of the disturbance is equal to the mean flow velocity. They are usually ignored when estimating the sound field, with their contribution assumed to be negligible. It is the aim of this paper to study fully both numerically and analytically a simple yet typical sheared ducted flow in order to distinguish between situations when the critical layer may or may not be ignored. The model is that of a linear-then-constant velocity profile with uniform density in a cylindrical duct, allowing for exact Green's function solutions in terms of Bessel functions and Frobenius expansions. It is found that the critical layer contribution decays algebraically in the constant flow part, with an additional contribution of constant amplitude when the source is in the boundary layer, an additional contribution of constant amplitude is excited, representing the hydrodynamic trailing vorticity of the source. This immediately triggers, for thin boundary layers, the inherent convective instability in the flow. Extra care is required for high frequencies as the critical layer can be neglected only together with the pole beneath it. For low frequencies this pole is trapped in the critical layer branch cut.

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Section: The Trailing Vorticity Field Behind a Point Source In Inmentioning

confidence: 87%

The critical layer in sheared flow

Darau

Rienstra

2011

17th AIAA/CEAS Aeroacoustics Conference (32nd AIAA Aeroacoustics Conference)

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“…We use the Cowling approximation [26] and neglect the perturbations of the gravitational acceleration. Following the standard method of nonmodal analysis (see [27] for a rigorous mathematical interpretation) we introduce the spatial Fourier harmonics (SFH) of the perturbations with time dependent phases:…”

Section: Physical Approachmentioning

confidence: 99%

Linear dynamics of the solar convection zone: Excitation of waves in unstably stratified shear flows

Chagelishvili¹,

Tevzadze²,

Goossens³

2000

AIP Conference Proceedings

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Abstract.In this paper we report on the nonresonant conversion of convectively unstable linear gravity modes into acoustic oscillation modes in shear flows. The convectively unstable linear gravity modes can excite acoustic modes with similar wave-numbers. The frequencies of the excited oscillations may be qualitatively higher than the temporal variation scales of the source flow, while the frequency spectra of the generated oscillations should be intrinsically correlated to the velocity field of the source flow. We anticipate that this nonresonant phenomenon can significantly contribute to the production of sound waves in the solar convection zone.

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“…This analysis, originally by Kelvin (1887), has had a wide distribution since 1990 (cf. Craik and Criminale 1986;Criminale and Drazin 1990;Gustavsson 1991;Butler and Farrell 1992;Chagelishvili et al 1997). By means of this so-called non-modal approach, substantial progress has been achieved in the understanding of shear flow phenomena in recent years.…”

Section: Introductionmentioning

confidence: 99%

Linear dynamics of non‐symmetric perturbations in geostrophic horizontal shear flows

Калашник¹,

Mamatsashvili²,

Chagelishvili³

et al. 2006

Quart J Royal Meteoro Soc

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SUMMARYThe linear dynamics of non-symmetric wave and vortex mode perturbations in spectrally stable geostrophic zonal flows with a constant horizontal shear along the meridional direction, when a fluid is incompressible and stratified, is investigated. Specific features of these dynamics are closely related to the non-normality of the linear operators governing perturbation evolution in shear flows and are well interpreted in the framework of the nonmodal approach-by tracing the linear dynamics of spatial Fourier harmonics of perturbations in time. If the Rossby number Ro < 1, there occurs an algebraic (asymptotically linear) amplification of non-symmetric shear internal waves. It is shown that at Ro > 1, in addition, there takes place an exponential/explosive transient growth of the waves that precedes the time interval of algebraic amplification. We also describe the evolution of pure vortex mode perturbations imposed initially on the mean flow. It is shown that at Ro ∼ 1, pure vortex (aperiodic) perturbations are able to gain basic flow energy and then generate non-symmetric shear internal waves. The studied linear phenomena are specific to geostrophic zonal flows and cast doubt on the filtering of fast wave perturbations in the traditional quasi-geostrophic models of geophysical hydrodynamics.

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The Evolution of Linearized Perturbations of Parallel Flows

Cited by 98 publications

References 13 publications

The critical layer in sheared flow

The critical layer in sheared flow

Linear dynamics of the solar convection zone: Excitation of waves in unstably stratified shear flows

Linear dynamics of non‐symmetric perturbations in geostrophic horizontal shear flows

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