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On the evolution of the turbulent spot in a laminar boundary layer with a favourable pressure gradient

Published online by Cambridge University Press:  26 April 2006

Y. Katz ,
A. Seifert  and
I. Wygnanski
Y. Katz
Affiliation:
Department of Fluid Mechanics and Heat Transfer, Tel-Aviv University, Ramat Aviv, Israel Present address: Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA.
A. Seifert
Affiliation:
Department of Fluid Mechanics and Heat Transfer, Tel-Aviv University, Ramat Aviv, Israel
I. Wygnanski
Affiliation:
Department of Fluid Mechanics and Heat Transfer, Tel-Aviv University, Ramat Aviv, Israel
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Abstract

The evolution of a turbulent spot in an accelerating laminar boundary-layer flow was investigated. The type of boundary layer chosen for this experiment resembles in every respect the flow in the vicinity of a stagnation point theoretically described by Falkner and Skan. The rate of growth of the spot was significantly inhibited by the favourable pressure gradient in all three directions. It became much shorter and narrower in comparison with a similar spot generated in a Blasius boundary layer at comparable distances from its origin and comparable Reynolds numbers. The celerities of its boundaries did not scale with the local free-stream velocity as they do in the absence of a pressure gradient. Dimensional analysis was used to identify and correlate the independent variables determining the size, the convection speed, and the relative rate of growth of this spot

The familiar arrowhead shape of the spot gave way to a rounded triangular shape with the trailing interface being straight and perpendicular to the direction of streaming. The familiar Tollmien-Schlichting wave packet was not observed in this pressure gradient because the surrounding boundary layer was very stable at the Re considered. Since the arrowhead shape of the spot is associated with the breakdown of the waves within the packet it cannot occur below the critical Re. The relative size of the ‘calmed region’ following the spot also diminished; however, one could only speculate as to the origin of this region.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 221 , December 1990 , pp. 1 - 22
Copyright
© 1990 Cambridge University Press

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