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Physics of Fluids / Volume 24 / Issue 6 / ARTICLES / Particulate, Multiphase, and Granular Flows

Phys. Fluids 24, 063302 (2012); http://dx.doi.org/10.1063/1.4729453 (18 pages)

The geometry of inertial particle mixing in urban flows, from deterministic and random displacement models

Wenbo Tang1, Brent Knutson1, Alex Mahalov1, and Reneta Dimitrova2

1School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona, 85287, USA
2Environmental Fluid Dynamics, University of Notre Dame, Notre Dame, Indiana 46556, USA

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(Received 4 August 2011; accepted 21 May 2012; published online 25 June 2012)

We use Lagrangian measures, depicted by finite-time Lyapunov exponents, to characterize transport patterns of inertial pollutant particles formed in urban flows. Motivated by actual events we focus on flows in realistic urban geometry. Both deterministic and stochastic particle transport patterns have been identified, as inertial Lagrangian coherent structures. For the deterministic case, the organizing structures are well-defined and we extract them at different hours of a day to reveal the variability of coherent patterns. For the stochastic case, we use a random displacement model for fluid particles and derive the governing equation for inertial particles to examine the change in organizing structures due to “zeroth-order” random noise. We find that, (1) the Langevin equation for inertial particles can be reduced to a random displacement model; (2) using random noise based on inhomogeneous turbulence, whose diffusivity is derived from k − ε models, major coherent structures survive to organize local flow patterns and weaker structures are smoothed out due to random motion.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. MATHEMATICAL FORMULATION
    1. The governing equations
    2. Reduction of Langevin equation to random displacement model
    3. Inertial Lagrangian coherent structures
  3. NUMERICAL DETAILS
    1. Urban wind model
    2. Details of deterministic and random displacement model
    3. Computation of FTLE and extraction of ILCS
  4. RESULTS
    1. Deterministic transport
    2. Stochastic transport
  5. DISCUSSIONS AND CONCLUSIONS

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KEYWORDS and PACS

Keywords

pattern formation, random noise, random processes, stochastic processes, turbulent diffusion

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.4729453

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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    References

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