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Three-dimensional evolution of vortical structures and associated flow bifurcations in the wake of two side-by-side square cylinders
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10.1063/1.2757712
/content/aip/journal/pof2/19/8/10.1063/1.2757712
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/8/10.1063/1.2757712
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Schematic representation of the physical setup and the coordinate system.

Image of FIG. 2.
FIG. 2.

Instantaneous streamwise flow behavior through different spanwise stations for , . (a) Streamlines on the symmetry plane ; (b) distribution of spanwise vortices on shows the antiphase synchronization of vortex shedding, leading to the formation of two antiphase streets; (c) streamlines on the plane ; (d) antiphase synchronization of spanwise vortices on .

Image of FIG. 3.
FIG. 3.

Instantaneous streamwise sectional flow behavior through different stations for , . (a) Streamlines on the symmetry plane ; (b) distribution of spanwise vortices on reveals near-wake in-phase synchronization of vortex shedding, the subsequent development of a binary vortex street within , and the complex two-street evolution thereafter; (c) streamlines on ; (d) in-phase distribution of vortices on .

Image of FIG. 4.
FIG. 4.

Instantaneous streamwise flow evolution reveals biased gap flow remains deflected towards the lower cylinder through different spanwise stations for , . (a) Streamlines on ; (b) streamlines on ; (c) streamlines on .

Image of FIG. 5.
FIG. 5.

Instantaneous spanwise vorticity distribution at different locations over the cylinder axes for , . (a) at ; (b) at ; (c) at .

Image of FIG. 6.
FIG. 6.

Instantaneous streamwise flow evolution through different stations shows spanwise nonuniform deflection of the biased gap flow for , . (a) Streamline pattern on ; (b) streamlines on ; (c) streamlines on .

Image of FIG. 7.
FIG. 7.

Instantaneous spanwise vorticity distribution at different locations shows their truly asymmetric growth over the cylinder axes at , . (a) at ; (b) at ; (c) at .

Image of FIG. 8.
FIG. 8.

Instantaneous streamwise sectional flows through different spanwise stations revealing complex 3D nature of growth of the Benard-Von Karman streets, with biased gap flow remaining deflected towards the upper cylinder at , . (a) Streamlines on ; (b) streamlines on ; (c) streamlines on .

Image of FIG. 9.
FIG. 9.

Instantaneous spanwise vorticity distribution at different locations over the cylinder axes for , . (a) at ; (b) at ; (c) at .

Image of FIG. 10.
FIG. 10.

Instantaneous streamwise flow evolution shows the formation of a closed form near wake just behind the lower cylinder and a far wider Benard-Von Karman-like street behind the upper cylinder at , . The gap flow is seen to remain deflected towards the lower cylinder. (a) Streamlines on ; (b) streamlines on ; (c) streamlines on .

Image of FIG. 11.
FIG. 11.

Instantaneous spanwise vorticity distribution at different locations shows the truly complex far-wake growth of the initially in-phase locked structures for , . (a) at ; (b) at ; (c) at .

Image of FIG. 12.
FIG. 12.

(Color) Three-dimensional mechanism of growth of the wake structure and associated flow bifurcations behind two square cylinders in side-by side arrangement with , . The two streamlines and issuing near the symmetry plane (from ) are seen to spiral in spanwise opposite directions along the vortex coreline . Fluid particles issuing from the left and right of are seen to spiral strictly towards the left end and right end , respectively, of the vortex coreline . Pressure variations along the critical streamlines and , the development of local pressure maximum over the midpoint of , and subsequent gradual pressure decrease along the left and right reveal such flow bifurcations are indeed initiated by the development of favorable pressure gradients along the vortex corelines.

Image of FIG. 13.
FIG. 13.

(Color online) Three-dimensional evolution of the in-phase wake and associated flow bifurcations behind two square cylinders with , . The streamlines spiraling around the vortex corelines and exhibit that the corresponding spanwise flows evolved through the symmetry-breaking mode-I Hopf bifurcation. Notably, flow along the vortex coreline is seen to bifurcate twice: once in each half of the coreline. Such flow bifurcations over a coreline is termed mode-II Hopf bifurcation.

Image of FIG. 14.
FIG. 14.

(Color) (a) Three-dimensional evolution of the biased flow and associated flow bifurcations at , . The spatial evolution of the streamlines and , and their oppositely spiraling behavior, reveal that flow over the vortex coreline evolves through a mode-I Hopf bifurcation. Evolution of the streamlines and reveals that the spanwise flow over the vortex coreline evolves through a mode-II Hopf bifurcation. Note also the local velocity fluctuations along and during their spatial evolution, and the localized formation of relatively larger vortical structures over , as jumps from the spanwise roller to the roller . (b) A side view of the vortical flow evolution at , , as presented in (a), with added streamlines , , and in it. The streamlines , , and reveal that the flow over the vortex coreline suffers a mode-I Hopf bifurcation. Note also, here, the kinked inward and kinked outward growth of the vortex corelines and during their spatial evolution.

Image of FIG. 15.
FIG. 15.

(Color) Three-dimensional evolution of the biased flow and associated flow bifurcations at , . The evolution of streamlines and with variable pressure distribution along them, and their oppositely spiraling nature over the vortex coreline show the presence of mode-I flow bifurcation in the wake of the cylinders. Similarly, the spanwise opposite spiraling nature of the streamlines and over the vortex coreline exhibits the dominance of mode-II Hopf bifurcation in the flipping regime.

Image of FIG. 16.
FIG. 16.

Instantaneous streamwise flow evolution through different stations shows the single-body-type growth of the downstream flow for , . (a) Streamline pattern on ; (b) streamlines on ; (c) streamlines on .

Image of FIG. 17.
FIG. 17.

Instantaneous spanwise vorticity distribution at different locations shows formation of a single Karman-like vortex street behind the cylinders at , . (a) at ; (b) at ; (c) at .

Image of FIG. 18.
FIG. 18.

(Color) Three-dimensional mechanism of growth of the wake and associated flow bifurcations behind two square cylinders with , . Oppositely spiraling nature of the streamlines and over the vortex coreline and that of and over the coreline demonstrate that the corresponding spanwise flows evolved through the symmetry-breaking mode-I Hopf bifurcation.

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/content/aip/journal/pof2/19/8/10.1063/1.2757712
2007-08-13
2014-04-18
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Three-dimensional evolution of vortical structures and associated flow bifurcations in the wake of two side-by-side square cylinders
http://aip.metastore.ingenta.com/content/aip/journal/pof2/19/8/10.1063/1.2757712
10.1063/1.2757712
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