Effects of streamwise-grooved spanwise-periodic roughness arrays on boundary-layer instability.
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| Title: | Effects of streamwise-grooved spanwise-periodic roughness arrays on boundary-layer instability. |
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| Authors: | Zheng, Jianing1, Wu, Xuesong2,3 x.wu@ic.ac.uk |
| Source: | Journal of Fluid Mechanics. 2/25/2026, Vol. 1029, following p1-38. 42p. |
| Subjects: | Boundary layer equations, Surface roughness, Atmospheric boundary layer, Laminar boundary layer, Flow instability |
| Abstract: | We investigate the impact of streamwise-grooved and spanwise-periodic surface roughness arrays on the lower-branch viscous Tollmien-Schlichting (TS) instability in the boundary layer over an otherwise flat plate. The streamwise length scale and spanwise spacing of the arrays are of O(L) and O(Re-3/8L), respectively, with the latter being comparable to the characteristic wavelength of the TS modes, where L is the distance from the leading edge of the plate to the peak location of the roughness arrays and Re denotes the Reynolds number based on L, assumed to be large. The characteristic height of the roughness arrays is of O(Re-3/8L), which is greater than the boundary-layer thickness and is the required asymptotic threshold for generating O(1) streaks. We show that this nonlinear streaky flow is governed by three-dimensional (3-D) boundary-layer equations supplemented by a Laplace equation in an inviscid upper deck. Prandtl's transformation is applied to convert the curved boundary to a flat one, which not only reduces computational complexity by avoiding meshing the geometry, but also shows that the spanwise undulation of the roughness arrays enhances transverse diffusion. The Laplace equation is solved to provide the spanwise pressure gradient and velocity, which drive the streaks. The boundary-layer equations are solved efficiently using a streamwise marching scheme. The linear viscous instability of the resulting streaky flow is analysed; by exploiting the asymptotic structure, the bi-global eigenvalue problem is reduced to a one-dimensional one, where the stability is found to be controlled by the spanwise-dependent wall shear and the shape function of the roughness arrays. The results suggest that two-dimensional and weakly 3-D low-frequency modes are stabilised, while most other modes are destabilised. The present formulation provides a convenient tool for predicting streaky flows induced by riblet-like roughness of fairly large height and furthermore assessing their viscous instability properties. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Effects of streamwise-grooved spanwise-periodic roughness arrays on boundary-layer instability. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zheng%2C+Jianing%22">Zheng, Jianing</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Wu%2C+Xuesong%22">Wu, Xuesong</searchLink><relatesTo>2,3</relatesTo><i> x.wu@ic.ac.uk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 2/25/2026, Vol. 1029, following p1-38. 42p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Boundary+layer+equations%22">Boundary layer equations</searchLink><br /><searchLink fieldCode="DE" term="%22Surface+roughness%22">Surface roughness</searchLink><br /><searchLink fieldCode="DE" term="%22Atmospheric+boundary+layer%22">Atmospheric boundary layer</searchLink><br /><searchLink fieldCode="DE" term="%22Laminar+boundary+layer%22">Laminar boundary layer</searchLink><br /><searchLink fieldCode="DE" term="%22Flow+instability%22">Flow instability</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We investigate the impact of streamwise-grooved and spanwise-periodic surface roughness arrays on the lower-branch viscous Tollmien-Schlichting (TS) instability in the boundary layer over an otherwise flat plate. The streamwise length scale and spanwise spacing of the arrays are of O(L) and O(Re-3/8L), respectively, with the latter being comparable to the characteristic wavelength of the TS modes, where L is the distance from the leading edge of the plate to the peak location of the roughness arrays and Re denotes the Reynolds number based on L, assumed to be large. The characteristic height of the roughness arrays is of O(Re-3/8L), which is greater than the boundary-layer thickness and is the required asymptotic threshold for generating O(1) streaks. We show that this nonlinear streaky flow is governed by three-dimensional (3-D) boundary-layer equations supplemented by a Laplace equation in an inviscid upper deck. Prandtl's transformation is applied to convert the curved boundary to a flat one, which not only reduces computational complexity by avoiding meshing the geometry, but also shows that the spanwise undulation of the roughness arrays enhances transverse diffusion. The Laplace equation is solved to provide the spanwise pressure gradient and velocity, which drive the streaks. The boundary-layer equations are solved efficiently using a streamwise marching scheme. The linear viscous instability of the resulting streaky flow is analysed; by exploiting the asymptotic structure, the bi-global eigenvalue problem is reduced to a one-dimensional one, where the stability is found to be controlled by the spanwise-dependent wall shear and the shape function of the roughness arrays. The results suggest that two-dimensional and weakly 3-D low-frequency modes are stabilised, while most other modes are destabilised. The present formulation provides a convenient tool for predicting streaky flows induced by riblet-like roughness of fairly large height and furthermore assessing their viscous instability properties. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Fluid Mechanics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1017/jfm.2026.11174 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 42 StartPage: 1 Subjects: – SubjectFull: Boundary layer equations Type: general – SubjectFull: Surface roughness Type: general – SubjectFull: Atmospheric boundary layer Type: general – SubjectFull: Laminar boundary layer Type: general – SubjectFull: Flow instability Type: general Titles: – TitleFull: Effects of streamwise-grooved spanwise-periodic roughness arrays on boundary-layer instability. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zheng, Jianing – PersonEntity: Name: NameFull: Wu, Xuesong IsPartOfRelationships: – BibEntity: Dates: – D: 25 M: 02 Text: 2/25/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00221120 Numbering: – Type: volume Value: 1029 Titles: – TitleFull: Journal of Fluid Mechanics Type: main |
| ResultId | 1 |
