A similarity transformation for a turbulent spot in a laminar boundary layer

The transition process of a small-amplitude wave packet, generated by a controlled short-duration air pulse, to the formation of a turbulent spot is traced experimentally in a laminar boundary layer. The vertical and spanwise structures of the flow field are mapped at several downstream locations. The measurements, which include all three velocity components, show three stages of transition. In the first stage, the wave packet can be treated as a superposition of two- and three-dimensional waves according to linear stability theory, and most of the energy is centred around a mode corresponding to the most amplified wave. In the second stage, most of the energy is transferred to oblique waves which are centred around a wave having half the frequency of the most amplified linear mode. During this stage, the amplitude of the wave packet increases from 0.5 % to 5 % of the free-stream velocity. In the final stage, a turbulent spot develops and the amplitude of the disturbance increases to 27 % of the free-stream velocity.Theoretical aspects of the various stages are considered. The amplitude and phase distributions of various modes of all three velocity components are compared with the solutions provided by linear stability theory. The agreement between the theoretical and measured distributions is very good during the first two stages of transition. Based on linear stability theory, it is shown that the two-dimensional mode of the streamwise velocity component is not necessarily the most energetic wave. While linear stability theory fails to predict the generation of the oblique waves in the second stage of transition, it is demonstrated that this stage appears to be governed by Craik-type subharmonic resonances.

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Boundary layer turbulence and freestream turbulence interface, turbulent spot and freestream turbulence interface, laminar boundary layer and freestream turbulence interface

Physics of Fluids ◽

10.1063/1.5093040 ◽

2019 ◽

Vol 31 (4) ◽

pp. 045104 ◽

Cited By ~ 8

Author(s):

Xiaohua Wu ◽

James M. Wallace ◽

Jean-Pierre Hickey

Keyword(s):

Boundary Layer ◽

Laminar Boundary Layer ◽

Freestream Turbulence ◽

Turbulent Spot ◽

Boundary Layer Turbulence

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On a turbulent ‘spot’ in a laminar boundary layer

Journal of Fluid Mechanics ◽

10.1017/s0022112076002747 ◽

1976 ◽

Vol 78 (04) ◽

pp. 785 ◽

Cited By ~ 131

Author(s):

I. Wygnanski ◽

M. Sokolov ◽

D. Friedman

Keyword(s):

Boundary Layer ◽

Laminar Boundary Layer ◽

Turbulent Spot

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On a Tollmien-Schlichting wave packet produced by a turbulent spot

Journal of Fluid Mechanics ◽

10.1017/s0022112079000756 ◽

1979 ◽

Vol 92 (3) ◽

pp. 505-528 ◽

Cited By ~ 55

Author(s):

I. Wygnanski ◽

J. H. Haritonidis ◽

R. E. Kaplan

Keyword(s):

Boundary Layer ◽

Wave Packet ◽

Shear Layer ◽

Laminar Boundary Layer ◽

Wave Speed ◽

Experimental Investigations ◽

Turbulent Spot ◽

Tollmien Schlichting ◽

Ordered Motion ◽

Intense Shear

Experimental investigations in the region following the passage of an isolated turbulent spot in a laminar boundary layer reveal the existence of a pair of oblique wave packets. These packets are swept at an angle of approximately 40°, and exhibit frequency and wave speed characteristics in agreement with predictions made for oblique Tollmien-Schlichting waves. No waves exist near the centreline of the spot.Several observations of the breakdown of this ordered motion into a new turbulent spot are shown. This breakdown is accompanied by the appearance of an intense shear layer inclined to the wall.

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Substructures in a turbulent spot

Journal of Fluid Mechanics ◽

10.1017/s0022112088003295 ◽

1988 ◽

Vol 197 ◽

pp. 389-414 ◽

Cited By ~ 41

Author(s):

R. Sankaran ◽

M. Sokolov ◽

R. A. Antonia

Keyword(s):

Boundary Layer ◽

Laminar Boundary Layer ◽

Leading Edge ◽

Simple Relation ◽

Sufficient Evidence ◽

Streamwise Direction ◽

Geometrical Construction ◽

Turbulent Spot ◽

Hairpin Vortices ◽

Streamwise Distance

Substructures within a turbulent spot which develops in a slightly heated laminar boundary layer have been identified using arrays of cold wires aligned in either a streamwise direction or in a direction normal to the wall. At any given streamwise distance from the spot origin, histograms of the number of detected substructures exhibit a peak, defining the most probable spot or the spot with the most likely number of substructures. The number of substructures in the most probable spot increases with streamwise distance but all substructures are convected at approximately the same velocity for any given distance from the wall. This velocity is approximately equal to that of the leading edge of the spot and increases slightly with distance from the wall. The increase in the number of substructures accounts for the streamwise growth of the spot. A simple relation is derived for determining the number of substructures at a particular streamwise station and a geometrical construction is proposed for identifying the origin of a new substructure. There is sufficient evidence for suggesting that the new substructures are formed near the trailing edge of the spot. The convection velocity, inclination and lengthscales of the substructures compare favourably with the corresponding characteristics of hairpin vortices.

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

Journal of Fluid Mechanics ◽

10.1017/s0022112090003469 ◽

1990 ◽

Vol 221 ◽

pp. 1-22 ◽

Cited By ~ 43

Author(s):

Y. Katz ◽

A. Seifert ◽

I. Wygnanski

Keyword(s):

Boundary Layer ◽

Pressure Gradient ◽

Laminar Boundary Layer ◽

Relative Rate ◽

Relative Size ◽

Stream Velocity ◽

Turbulent Spot ◽

Rate Of Growth ◽

Tollmien Schlichting ◽

Convection Speed

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 spotThe 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.

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