2013
DOI: 10.1017/jfm.2013.421
|View full text |Cite
|
Sign up to set email alerts
|

On continuous spectra of the Orr–Sommerfeld/Squire equations and entrainment of free-stream vortical disturbances

Abstract: Small-amplitude perturbations are governed by the linearized Navier-Stokes equations, which are, for a parallel or nearly parallel shear flow, customarily reduced to the Orr-Sommerfeld (O-S) and Squire equations. In this paper, we consider continuous spectra (CS) of the O-S and Squire operators for the Blasius and asymptotic suction boundary layers, and address the issue of whether and when continuous modes can represent free-stream vortical disturbances and their entrainment into the shear layer. For the Blas… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2
1

Citation Types

2
55
0

Year Published

2014
2014
2023
2023

Publication Types

Select...
8

Relationship

2
6

Authors

Journals

citations
Cited by 42 publications
(57 citation statements)
references
References 35 publications
2
55
0
Order By: Relevance
“…We focus on the acoustic part of the perturbation. Vortical and entropy waves are also present (see Appendix A), but they are absorbed by a thin layer located at the outer edge of the boundary layer without entering the latter (Dong & Wu 2013; see also Maslov et al 2010, where such features were observed experimentally). The acoustic wave is governed by the (quasi-steady) Euler equations linearized about the uniform flow, among which the momentum equation in the y-direction reads…”
Section: Upper Deckmentioning
confidence: 93%
See 1 more Smart Citation
“…We focus on the acoustic part of the perturbation. Vortical and entropy waves are also present (see Appendix A), but they are absorbed by a thin layer located at the outer edge of the boundary layer without entering the latter (Dong & Wu 2013; see also Maslov et al 2010, where such features were observed experimentally). The acoustic wave is governed by the (quasi-steady) Euler equations linearized about the uniform flow, among which the momentum equation in the y-direction reads…”
Section: Upper Deckmentioning
confidence: 93%
“…It is worth noting that the streamwise and spanwise velocity components of the vorticity wave are much greater than those of the T-S wave. As its phase speed is approximately unity, this part of disturbance is trapped in a thin layer at the outer reach of the boundary layer and hence has little influence on the latter (Dong & Wu 2013). For the O(δ) disturbance in the expansion (4.1), it suffices to consider p 2 and v 2 only, which are governed by the equations …”
Section: Upper Deckmentioning
confidence: 99%
“…This layer (which was not included in some of the previous studies) is expected to act as a kind of buffer zone that prevents the high-frequency/small-scale disturbances in region IV from penetrating into region III (see [7]). It did not appear in the analyses in [8,18] because the region IV disturbances were of low frequency or completely steady in those papers, and it was not included in [11] because the low-frequency components could be treated independently of the high-frequency components in the linearized flow investigated in that paper.…”
Section: Overall Flow Structurementioning
confidence: 99%
“…Recently, Dong & Wu (2013) considered the boundary-layer response to FSVD with wavelength comparable with the local boundary-layer thickness. Interestingly, despite the relatively short wavelength non-parallelism appears at leading order in the edge layer, which is located at the outer edge of the boundary layer, and controls the entrainment process.…”
Section: Introductionmentioning
confidence: 99%
“…Since continuous modes of these equations have the same phase speeds as free-stream vortical disturbances, it has been suggested that each continuous mode represents a Fourier component in the vortical disturbance with its eigenfunction characterizing the distribution of the perturbation entrained into the boundary layer (Grosch & Salwen 1978). This interpretation was examined by Dong & Wu (2013). They noted that continuous modes exhibit two peculiar features: 'entanglement of Fourier components' and 'abnormal anisotropy'.…”
Section: Introductionmentioning
confidence: 99%