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The geometry of inertial particle mixing in urban flows, from deterministic and random displacement models
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10.1063/1.4729453
/content/aip/journal/pof2/24/6/10.1063/1.4729453
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/6/10.1063/1.4729453

Figures

Image of FIG. 1.
FIG. 1.

Three-dimensional view of backward-time ILCS at 6 a.m. on January 16, 2009. (a) PM2.5. (b) PM10. Note the removal of separation structures at the roof top with PM10.

Image of FIG. 2.
FIG. 2.

Attracting ILCS for deterministic dynamics evaluated at 6 a.m. on January 16, 2009. The two panels show structures associated with different particle sizes at Z = 1 m. (a) PM2.5. (b) PM10.

Image of FIG. 3.
FIG. 3.

Repelling ILCS for deterministic dynamics evaluated at 6 a.m. on January 16, 2009. The two panels show structures associated with different particle sizes at Z = 1 m. (a) PM2.5. (b) PM10.

Image of FIG. 4.
FIG. 4.

Particle trajectories initiated near forward-time ILCS upwind of building A. Black: released at Z = 20 m. Mid-grey (green): release at Z = 3 m. (a) Idealized fluid tracer. (b) PM2.5. (c) PM20.

Image of FIG. 5.
FIG. 5.

Comparisons of backward-time FTLE for PM2.5 at two different times on January 16, 2009, at Z = 1 m. (a) 6 a.m. (b) 6 p.m.

Image of FIG. 6.
FIG. 6.

Comparisons of forward-time FTLE for PM2.5 at two different times on January 16, 2009, at Z = 1 m. (a) 6 a.m. (b) 6 p.m.

Image of FIG. 7.
FIG. 7.

Comparisons among stochastic and deterministic trajectories. (a) Comparisons on the mean trajectories. Mid-grey (red): mean from full Maxey-Riley equations. Dark-grey (blue): mean from inertial equations. Black: deterministic equations. Solid: Backward-time trajectories. Dashed: Forward-time trajectories. (b) Comparisons between the full equations and inertial equations for random realizations. Mid-grey (red): full equations, forward-time. Dark-grey (blue): inertial equations, forward-time. Light-grey (cyan): inertial equations, backward-time. Backward-time realizations with the full equations are not shown as they become unstable and leave the domain quickly.

Image of FIG. 8.
FIG. 8.

Forward-time stochastic ILCS near the tall building at Z = 2 m for PM2.5 on February 15, 2009. (a) Deterministic. (b) 0.25 of the full eddy diffusivity. (c) 0.5 of the full eddy diffusivity. (d) Full eddy diffusivity.

Image of FIG. 9.
FIG. 9.

Backward-time stochastic ILCS near the tall building at Z = 2 m for PM2.5 on February 15, 2009. (a) Deterministic. (b) 0.25 of the full eddy diffusivity. (c) 0.5 of the full eddy diffusivity. (d) Full eddy diffusivity.

Image of FIG. 10.
FIG. 10.

Comparison between deterministic and stochastic ILCS near the tall building at Z = 2 m for PM10. (a) Deterministic, forward-time. (b) Deterministic, backward-time. (c) Full eddy diffusivity, forward-time. (d) Full eddy diffusivity, backward-time.

Tables

Generic image for table
Table I.

Correlation of stochastic and deterministic FTLE.

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/content/aip/journal/pof2/24/6/10.1063/1.4729453
2012-06-25
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The geometry of inertial particle mixing in urban flows, from deterministic and random displacement models
http://aip.metastore.ingenta.com/content/aip/journal/pof2/24/6/10.1063/1.4729453
10.1063/1.4729453
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