A class of exact Navier-Stokes solutions for homogeneous flat-plate boundary layers and their linear stability

John, Michael O.; Obrist, Dominik; Kleiser, Leonhard (2014). A class of exact Navier-Stokes solutions for homogeneous flat-plate boundary layers and their linear stability. Journal of fluid mechanics, 752, pp. 462-484. Cambridge University Press 10.1017/jfm.2014.346

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We introduce a new boundary layer formalism on the basis of which a class of exact solutions to the Navier–Stokes equations is derived. These solutions describe laminar boundary layer flows past a flat plate under the assumption of one homogeneous direction, such as the classical swept Hiemenz boundary layer (SHBL), the asymptotic suction boundary layer (ASBL) and the oblique impingement boundary layer. The linear stability of these new solutions is investigated, uncovering new results for the SHBL and the ASBL. Previously, each of these flows had been described with its own formalism and coordinate system, such that the solutions could not be transformed into each other. Using a new compound formalism, we are able to show that the ASBL is the physical limit of the SHBL with wall suction when the chordwise velocity component vanishes while the homogeneous sweep velocity is maintained. A corresponding non-dimensionalization is proposed, which allows conversion of the new Reynolds number definition to the classical ones. Linear stability analysis for the new class of solutions reveals a compound neutral surface which contains the classical neutral curves of the SHBL and the ASBL. It is shown that the linearly most unstable Görtler–Hämmerlin modes of the SHBL smoothly transform into Tollmien–Schlichting modes as the chordwise velocity vanishes. These results are useful for transition prediction of the attachment-line instability, especially concerning the use of suction to stabilize boundary layers of swept-wing aircraft.

Item Type:

Journal Article (Original Article)

Division/Institute:

10 Strategic Research Centers > ARTORG Center for Biomedical Engineering Research > ARTORG Center - Cardiovascular Engineering (CVE)

UniBE Contributor:

Obrist, Dominik

Subjects:

500 Science > 510 Mathematics
500 Science > 530 Physics
600 Technology > 620 Engineering

ISSN:

1469-7645

Publisher:

Cambridge University Press

Language:

English

Submitter:

Dominik Obrist

Date Deposited:

12 Jun 2015 10:21

Last Modified:

30 Sep 2016 17:17

Publisher DOI:

10.1017/jfm.2014.346

BORIS DOI:

10.7892/boris.69379

URI:

https://boris.unibe.ch/id/eprint/69379

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