Locating an atmospheric contamination source using slow manifolds

Wenbo Tang, George Haller, Jong Jin Baik, Young Hee Ryu

Research output: Contribution to journalArticlepeer-review


Finite-size particle motion in fluids obeys the Maxey-Riley equations, which become singular in the limit of infinitesimally small particle size. Because of this singularity, finding the source of a dispersed set of small particles is a numerically ill-posed problem that leads to exponential blowup. Here we use recent results on the existence of a slow manifold in the Maxey-Riley equations to overcome this difficulty in source inversion. Specifically, we locate the source of particles by projecting their dispersed positions on a time-varying slow manifold, and by advecting them on the manifold in backward time. We use this technique to locate the source of a hypothetical anthrax release in an unsteady three-dimensional atmospheric wind field in an urban street canyon.

Original languageEnglish
Article number043302
JournalPhysics of Fluids
Issue number4
Publication statusPublished - 2009

Bibliographical note

Funding Information:
This work was supported by the Air Force Office of Scientific Research under Grant No FA9550-06-1-0101. We are grateful to Themis Sapsis for helpful discussions. We also thank two anonymous referees for their valuable critiques and comments.

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes


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