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Low-dimensional model of spatial shear layers
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10.1063/1.3678016
/content/aip/journal/pof2/24/1/10.1063/1.3678016
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/1/10.1063/1.3678016

Figures

Image of FIG. 1.
FIG. 1.

Schematic of the two-dimensional free shear layer simulation.

Image of FIG. 2.
FIG. 2.

Snapshots of the shear layer at different times: (a) t=50.4, (b) t=60, (c) t=69.6, (d) t=79.2, (e) t=88.8, and (f) . Contours show vorticity .

Image of FIG. 3.
FIG. 3.

The thickness growth along x direction while the shear layer is developing; sample vortex structure is shown for comparison.

Image of FIG. 4.
FIG. 4.

for POD modes at : (a) and (b) . The thin solid line represents the real value, the thin dashed line represents the imaginary value, and the thick solid line represents the absolute value.

Image of FIG. 5.
FIG. 5.

of the instability mode for . The thin solid line represents the real value, the thin dashed line represents the imaginary value, and the thick solid line represents the absolute value.

Image of FIG. 6.
FIG. 6.

for POD modes at : (a) and (b) . The thin solid line represents the real value, the thin dashed line represents the imaginary value, and the thick solid line represents the absolute value.

Image of FIG. 7.
FIG. 7.

of the instability mode for . The thin solid line represents the real value, the thin dashed line represents the imaginary value, and the thick solid line represents the absolute value.

Image of FIG. 8.
FIG. 8.

Comparison of (a) direct projection from DNS data to (b) 2-mode model results and (c) 4-mode model results: _____, real part of mode coefficient and ; _ _ _ _, real part of mode coefficient and ; and _ _ _, shear-layer thickness .

Image of FIG. 9.
FIG. 9.

Relation between the shear layer thickness variation and the sudden change of the phase difference of the first two POD modes: (a) from the projection of full simulation, (b) from the solution of 2-mode model, (c) from the solution of 4-mode model. Notations are _______ phase difference between and , phase difference between and , and _ _ _ the shear layer thickness .

Image of FIG. 10.
FIG. 10.

Comparison of flow fields at time visualized from: (a) DNS data, (b) projection of DNS data onto 2 POD modes at , (c) 2-mode model, (d) projection of DNS data onto all 4 modes, and (e) 4-mode model. Contours show vorticity .

Image of FIG. 11.
FIG. 11.

Comparison of forcing at frequency with mode (1,1): different amplitudes of forcing are applied at 0 (a), 0.5 (b), 1.0 (c), and 1.5 (d); _______, real part of mode coefficient and ; _ _ _ _, real part of mode coefficient and ; _ _ _, shear-layer thickness .

Image of FIG. 12.
FIG. 12.

Comparison of forcing at frequency with mode (2,1): different amplitudes of forcing are applied at 0 (a), 1.0 (b), 2.0 (c), and 3.0 (d); _______, real part of mode coefficient and ; _ _ _ _, real part of mode coefficient and ; _ _ _, shear-layer thickness .

Image of FIG. 13.
FIG. 13.

Vorticity field snapshots (top) (at , 648, 672, 696, 720, 744, 768, 792, and 816) and average thickness variations (bottom) from: (a) DNS projection on 4 modes, (b) 4-mode model, (c) 4-mode model with excitation at k=1, and (d) 4-mode model with excitation at k=2. Contours show vorticity .

Tables

Generic image for table
Table I.

Energy captured by different POD modes.

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/content/aip/journal/pof2/24/1/10.1063/1.3678016
2012-01-31
2014-04-25
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Low-dimensional model of spatial shear layers
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/1/10.1063/1.3678016
10.1063/1.3678016
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