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The critical layer in quadratic flow boundary layers over acoustic linings
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King, Matthew J., Brambley, Edward J., Liupekevicius, Renan, Radia, Miren, Lafourcade, Paul and Shah, Tauqeer H. (2022) The critical layer in quadratic flow boundary layers over acoustic linings. Journal of Fluid Mechanics, 950 . A8. doi:10.1017/jfm.2022.753 ISSN 0022-1120.
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Official URL: https://doi.org/10.1017/jfm.2022.753
Abstract
A straight cylindrical duct is considered containing an axial mean flow that is uniform everywhere except within a boundary layer near the wall, which need not be thin. Within this boundary layer the mean flow varies parabolically. The linearized Euler equations are Fourier transformed to give the Pridmore-Brown equation, for which the Green's function is constructed using Frobenius series. The critical layer gives a non-modal contribution from the continuous spectrum branch cut, and dominates the downstream pressure perturbation in certain cases, particularly for thicker boundary layers. The continuous spectrum branch cut is also found to stabilize what are otherwise convectively unstable modes by hiding them behind the branch cut. Overall, the contribution from the critical layer is found to give a neutrally stable non-modal wave when the source is located within the sheared flow region, and to decay algebraically along the duct as O(x−5/2) for a source located with the uniform flow region. The Frobenius expansion, in addition to being numerically accurate close to the critical layer where other numerical methods lose accuracy, is also able to locate modal poles hidden behind the branch cut, which other methods are unable to find; this includes the stabilized hydrodynamic instability. Matlab code is provided to compute the Green's function.
| Item Type: | Journal Article | ||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics T Technology > TA Engineering (General). Civil engineering (General) |
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| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics Faculty of Science, Engineering and Medicine > Engineering > WMG (Formerly the Warwick Manufacturing Group) |
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| Library of Congress Subject Headings (LCSH): | Functions, Sound pressure -- Mathematical models, Fluid mechanics , Boundary layer | ||||||||||||||||||
| Journal or Publication Title: | Journal of Fluid Mechanics | ||||||||||||||||||
| Publisher: | Cambridge University Press | ||||||||||||||||||
| ISSN: | 0022-1120 | ||||||||||||||||||
| Official Date: | 10 November 2022 | ||||||||||||||||||
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| Volume: | 950 | ||||||||||||||||||
| Number of Pages: | 45 | ||||||||||||||||||
| Article Number: | A8 | ||||||||||||||||||
| DOI: | 10.1017/jfm.2022.753 | ||||||||||||||||||
| Status: | Peer Reviewed | ||||||||||||||||||
| Publication Status: | Published | ||||||||||||||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||||||||||||||
| Date of first compliant deposit: | 12 September 2022 | ||||||||||||||||||
| Date of first compliant Open Access: | 19 October 2022 | ||||||||||||||||||
| RIOXX Funder/Project Grant: |
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