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

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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 Reconsidered. 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.

Original languageEnglish (US)
Pages (from-to)1-22
Number of pages22
JournalJournal of Fluid Mechanics
Volume221
DOIs
StatePublished - 1990
Externally publishedYes

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laminar boundary layer
Laminar boundary layer
Pressure gradient
pressure gradients
boundary layers
Boundary layers
Tollmien-Schlichting waves
Wave packets
boundary layer flow
stagnation point
Boundary layer flow
dimensional analysis
free flow
wave packets
Reynolds number
convection
breakdown
Experiments

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Condensed Matter Physics

Cite this

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title = "On the evolution of the turbulent spot in a laminar boundary layer with a favourable pressure gradient",
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 Reconsidered. 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.",
author = "Y. Katz and Wygnanski, {Israel J}",
year = "1990",
doi = "10.1017/S0022112090003469",
language = "English (US)",
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journal = "Journal of Fluid Mechanics",
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publisher = "Cambridge University Press",

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AU - Wygnanski, Israel J

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N2 - 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 Reconsidered. 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.

AB - 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 Reconsidered. 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.

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