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Algebraic growth of disturbances in a laminar boundary layer
1981 (English)In: Physics of Fluids (1958-1988), ISSN 0031-9171, Vol. 24, no 6, p. 1000-1004Article in journal (Refereed) Published
Abstract [en]

The temporal evolution of small three-dimensional disturbances with a large streamwise scale in viscous, parallel, semi-bounded flows is studied. In the limit of the initial disturbance being independent of the streamwise coordinate, the vertical velocity component consists solely of a continuous spectrum part. Tollmien-Schlichting waves do not appear in this special case. The streamwise perturbation velocity is obtained by solving a forced initial value problem. While the vertical velocity remains constant for small times, the streamwise perturbation velocity exhibits a linear growth due to the forcing. Eventually, viscous dissipation becomes dominant and the disturbance decays. Asymptotic solutions valid for small and large times are presented. The relation of these results to the longitudinal streaky structure found in many shear flows is discussedThe temporal evolution of small three-dimensional disturbances with a large streamwise scale in viscous, parallel, semi-bounded flows is studied. In the limit of the initial disturbance being independent of the streamwise coordinate, the vertical velocity component consists solely of a continuous spectrum part. Tollmien-Schlichting waves do not appear in this special case. The streamwise perturbation velocity is obtained by solving a forced initial value problem. While the vertical velocity remains constant for small times, the streamwise perturbation velocity exhibits a linear growth due to the forcing. Eventually, viscous dissipation becomes dominant and the disturbance decays. Asymptotic solutions valid for small and large times are presented. The relation of these results to the longitudinal streaky structure found in many shear flows is discussed. © 1981 American Institute of Physics.

Abstract [en]

The temporal evolution of small three-dimensional disturbances with a large streamwise scale in viscous, parallel, semi-bounded flows is studied. In the limit of the initial disturbance being independent of the streamwise coordinate, the vertical velocity component consists solely of a continuous spectrum part. Tollmien-Schlichting waves do not appear in this special case. The streamwise perturbation velocity is obtained by solving a forced initial value problem. While the vertical velocity remains constant for small times, the streamwise perturbation velocity exhibits a linear growth due to the forcing. Eventually, viscous dissipation becomes dominant and the disturbance decays. Asymptotic solutions valid for small and large times are presented. The relation of these results to the longitudinal streaky structure found in many shear flows is discussed. © 1981 American Institute of Physics.

Place, publisher, year, edition, pages
1981. Vol. 24, no 6, p. 1000-1004
National Category
Fluid Mechanics and Acoustics
Research subject
Fluid Mechanics
Identifiers
URN: urn:nbn:se:ltu:diva-5164DOI: 10.1063/1.863490Local ID: 331ecd10-096f-11de-9f31-000ea68e967bOAI: oai:DiVA.org:ltu-5164DiVA, id: diva2:978038
Note
Upprättat; 1981; 20090305 (bajo)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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Gustavsson, Håkan

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