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Streak interactions and breakdown in boundary layer flows
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10.1063/1.2838594
/content/aip/journal/pof2/20/2/10.1063/1.2838594
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/2/10.1063/1.2838594
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

The inflow streaky perturbation, , for and . The background depicts the streamwise vorticity with shading ranging from black to white for negative and positive values, respectively. The maximum value of the vorticity is . The lines display streamwise velocity perturbation. Minimum contour line , contour spacing 0.025. Dashed lines are used for negative values.

Image of FIG. 2.
FIG. 2.

Streamwise growth of the streak amplitude computed from the linear boundary-layer equations. The inflow amplitude is set to the value used in the simulations of breakdown. (—): ; (----): (— - —): ; (—): ; (----): .

Image of FIG. 3.
FIG. 3.

Sketch of the parameters defining the streak interactions: The relative spanwise phase and the angle between the axis of the two colliding streaks varied through the frequency of the upstream streak.

Image of FIG. 4.
FIG. 4.

(a) Time behavior of the averaged spanwise velocity for the symmetric and asymmetric breakdown of two straight streaks obtained with relative spanwise phase of and , respectively. (b) Evolution of for different initial distances between the colliding streaks, , 35, and 45 at .

Image of FIG. 5.
FIG. 5.

Evolution of the streaky structures during the symmetric breakdown, , depicted at time , 400, 450, and 500 [(a)–(d)]. The light (gold) color displays surfaces of positive streamwise velocity, whereas low-speed fluid is depicted in a dark (blue) color. The values shown are in (a) and (b), in (c), and in (d).

Image of FIG. 6.
FIG. 6.

The shear-layer instability developing during the symmetric streak interaction , depicted by negative (black) and positive (white) contour levels, is the streamwise perturbation velocity in the plane at time , 400, and 450. Contour spacing is 0.02.

Image of FIG. 7.
FIG. 7.

The high-frequency perturbation growing during the symmetric streak interaction, displayed at . In both figures, the light (gold) color displays surfaces of positive streamwise velocity , whereas low-speed fluid is depicted in a dark (blue) color. (a) Surface of constant wall-normal velocity perturbation . (b) Surface of constant spanwise velocity perturbation , with black for negative values and white for positive values.

Image of FIG. 8.
FIG. 8.

Vortical structures characteristic of the symmetric breakdown at . In (a) dark (blue) surfaces represent low-streamwise velocity while light gray (gold) surfaces depict high-speed regions . Gray (green) represents negative values of , used to identify vortical structures.

Image of FIG. 9.
FIG. 9.

Vortical structures at the late stages of the symmetric breakdown, . Dark (blue) surfaces represent low-streamwise velocity while light gray (gold) surfaces depict high-speed regions . Gray (green) represents negative values of .

Image of FIG. 10.
FIG. 10.

Evolution of the streamwise vorticity during the symmetric breakdown, , depicted at time , 400, and 450 [(a)–(c)]. Positive and negative vorticity are represented in white and black, respectively. The light (gold) color displays surfaces of positive streamwise velocity, whereas low-speed fluid is depicted in a dark (blue) color. The values shown are ; in (a), in (b), and in (c).

Image of FIG. 11.
FIG. 11.

(a) Streamwise vorticity and (b) vortex tilting term for the symmetric breakdown, , depicted at time . Positive and negative vorticity are represented in white and black, respectively, whereas light (gold) and dark (blue) colors are used to display surfaces of positive and negative values of the tilting. The values shown are and .

Image of FIG. 12.
FIG. 12.

Streamwise vorticity and vortex stretching term for the symmetric breakdown, , depicted at time and . Contour lines represent the stretching term (contour levels 0.01), while the background color indicates the streamwise vorticity.

Image of FIG. 13.
FIG. 13.

Evolution of the streaky structures during the asymmetric breakdown, , depicted at time , 400, 450, and 500. The light (gold) color displays surfaces of positive streamwise velocity, whereas low-speed fluid is depicted in a dark (blue) color. The values shown are in (a), in (b) and (c), and in (d).

Image of FIG. 14.
FIG. 14.

The asymmetric streak interaction in the cross-stream plane. Negative (black) and positive (white) contour levels of the streamwise perturbation velocity with contour spacing 0.02 are reported at time , 400, and 450 and streamwise locations , 60, and 75, respectively. The initial spanwise shift between the two streaks is .

Image of FIG. 15.
FIG. 15.

The high-frequency perturbation growing during the asymmetric streak interaction, displayed at . In both figures, the light (gold) color displays surfaces of positive streamwise velocity , whereas low-speed fluid is depicted in a dark (blue) color. (a) Surface of constant wall-normal velocity perturbation . (b) Surface of constant spanwise velocity perturbation , with black for negative values and white for positive values.

Image of FIG. 16.
FIG. 16.

Vortical structures characteristic of the asymmetric breakdown, , at and . In (a) dark (blue) surfaces represent low-streamwise velocity while light gray (gold) surfaces depict high-speed regions . Gray (green) represents negative values of .

Image of FIG. 17.
FIG. 17.

Evolution of the streamwise vorticity during the asymmetric breakdown, , depicted at time , 400, and 450 [(a)–(c)]. Positive and negative vorticity are represented in white and black, respectively. The light (gold) color displays surfaces of positive streamwise velocity, whereas low-speed fluid is depicted in a dark (blue) color. The values shown are ; in (a), in (b), and in (c).

Image of FIG. 18.
FIG. 18.

(a) Streamwise vorticity and (b) vortex tilting term for the asymmetric breakdown, , depicted at time . Positive and negative vorticity are represented in white and black, respectively, whereas light (gold) and dark (blue) colors are used to display surfaces of positive and negative values of the tilting. The values shown are and .

Image of FIG. 19.
FIG. 19.

Streamwise vorticity and vortex stretching term for the asymmetric breakdown, , depicted at time and . Contour lines represent the stretching term (contour levels 0.01), while the background color indicates the streamwise vorticity.

Image of FIG. 20.
FIG. 20.

Surfaces of constant shear , with at time , 400, and 450 for the symmetric breakdown, . The values shown are in (a) and (b), whereas the surface is depicted in (c).

Image of FIG. 21.
FIG. 21.

Surfaces of constant shear at time , 400, and 500 for the symmetric breakdown, . The values shown are in (a) and (b), whereas the surface is depicted in (c). Note that the flow pattern is now viewed from the opposite side when compared to Fig. 13 and following (positive direction toward the reader).

Image of FIG. 22.
FIG. 22.

Diagram of the different breakdown scenarios observed as a function of the frequency of the upstream streak (, 1, 2, 3, and ) and of . White areas: No breakdown. Gray shade: Asymmetric breakdown. Black regions: Symmetric breakdown.

Image of FIG. 23.
FIG. 23.

The streaky structures at breakdown for (a) ; (b) ; (c) . Time and . The light (gold) color displays surfaces of positive streamwise velocity, whereas low-speed fluid is depicted in a dark (blue) color. The values shown are in (a) and in (b) and (c).

Image of FIG. 24.
FIG. 24.

Wall-normal maximum and minimum of the streamwise velocity perturbation of the colliding streaks for the symmetric breakdown in the center plane at and 500. The amplitude of the downstream low-speed region is depicted by the dashed line, while the solid line is used to represent the incoming high-momentum fluid . Thick lines indicates the perturbation at time .

Image of FIG. 25.
FIG. 25.

Amplitude of the difference between the streamwise velocity perturbation at the centers of the interacting high- and low-speed regions at marginal conditions for breakdown. Values extracted at . (—) and (— - —): Symmetric scenario for different values of the initial distance between the streaks. (----): Asymmetric breakdown.

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/content/aip/journal/pof2/20/2/10.1063/1.2838594
2008-02-28
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Streak interactions and breakdown in boundary layer flows
http://aip.metastore.ingenta.com/content/aip/journal/pof2/20/2/10.1063/1.2838594
10.1063/1.2838594
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