266
Air Pollution and Turbulence: Modeling and Applications
a wide range of dispersion models can be developed and tested, in view of their use
in air quality applications.
From a Lagrangian point of view, we investigated the problem of relative dispersion in a neutral boundary layer simulated by means of LES. In particular, we
focused our study on relative dispersion and on Richardson’s law driving the separation of particle pairs.
In general, there are many diffi culties in such analysis, as it is hard to simulate a PBL with a suffi ciently extended inertial range of scales. Another diffi culty
arises from the problem of the overlap between dispersion regimes, which is why
we applied a nonstandard technique (FSLE) coming from the study of dynamical
systems to better identify Richardson’s law. The FSLE is a powerful analysis tool for
studying relative dispersion, as shown in many recent works. In this case, the FSLE
analysis allowed us to detect a clean scaling range where the expected Richardson’s
law was observed. This kind of analysis was fi rst carried out in a neutral boundary layer, without any subgrid model. In this case, we found that the value of the
Richardson constant is C 2 0.5. This estimate is compatible with recent results that
fi x it within the [0.1–1] range.
The new strategy, FSLE, for studying the problem of PBL relative dispersion in
LES fi elds has therefore provided positive results with respect to standard methods.
A correct description of the behavior of pair separation provides clear advantages for
understanding pollutant dispersion.
Finally, we have confi rmed that LES are a powerful instrument to simulate
those turbulent structures fundamental to describing dispersion phenomena within
the PBL.
REFERENCES
Ahlberg, J.H., E.N. Nilson, and J.L. Walsh. 1967. The Theory of Splines and Their Applications.
Academic Press, New York.
Andren, A., A.R. Brown, J. Graf, P.J. Mason, C.H. Moeng, F.T.M. Nieuwstadt, and
U. Schumann. 1994. Large eddy simulation of a neutrally stratifi ed boundary layer: A
comparison of four computer codes. Q. J. R. Meteorol. Soc. 120: 1457–1484.
Boffetta, G. and I.M. Sokolov. 2002. Relative dispersion in fully developed turbulence: The
Richardson’s law and intermittency corrections. Phys. Rev. Lett. 88: 494–501
Boffetta, G., A. Celani, M. Cencini, G. Lacorata, and A. Vulpiani. 2000. Non Asymptotic
properties of transport and mixing, Chaos 10: 1–9.
Deardorff, J.W. 1970. Numerical simulation of turbulent channel fl ow at large Reynolds
number. J. Fluid Mech. 41: 452–480.
Deardorff, J.W. 1972. Numerical investigation of neutral and unstable planetary boundary
layers. J. Atmos. Soc., 29: 91–115.
Forester, C.K. 1979. Higher order monotonic convective difference schemes. J. Comput. Phys.
23: 1–22.
Fox, D.G. and S.A. Orszag. 1973. Pseudo-spectral approximation of two-dimensional turbulence. J. Comput. Phys. 11: 612–619.
Gioia, G., G. Lacorata, E.P. Marques Filho, A. Mazzino, and U. Rizza. 2004. The Richardson’s
law in large-eddy simulations of boundary layer fl ows. Bound. Layer Meteorol. 113:
187–199.
© 2010 by Taylor and Francis Group, LLC
Air Pollution and Turbulence: Modeling and Applications
a wide range of dispersion models can be developed and tested, in view of their use
in air quality applications.
From a Lagrangian point of view, we investigated the problem of relative dispersion in a neutral boundary layer simulated by means of LES. In particular, we
focused our study on relative dispersion and on Richardson’s law driving the separation of particle pairs.
In general, there are many diffi culties in such analysis, as it is hard to simulate a PBL with a suffi ciently extended inertial range of scales. Another diffi culty
arises from the problem of the overlap between dispersion regimes, which is why
we applied a nonstandard technique (FSLE) coming from the study of dynamical
systems to better identify Richardson’s law. The FSLE is a powerful analysis tool for
studying relative dispersion, as shown in many recent works. In this case, the FSLE
analysis allowed us to detect a clean scaling range where the expected Richardson’s
law was observed. This kind of analysis was fi rst carried out in a neutral boundary layer, without any subgrid model. In this case, we found that the value of the
Richardson constant is C 2 0.5. This estimate is compatible with recent results that
fi x it within the [0.1–1] range.
The new strategy, FSLE, for studying the problem of PBL relative dispersion in
LES fi elds has therefore provided positive results with respect to standard methods.
A correct description of the behavior of pair separation provides clear advantages for
understanding pollutant dispersion.
Finally, we have confi rmed that LES are a powerful instrument to simulate
those turbulent structures fundamental to describing dispersion phenomena within
the PBL.
REFERENCES
Ahlberg, J.H., E.N. Nilson, and J.L. Walsh. 1967. The Theory of Splines and Their Applications.
Academic Press, New York.
Andren, A., A.R. Brown, J. Graf, P.J. Mason, C.H. Moeng, F.T.M. Nieuwstadt, and
U. Schumann. 1994. Large eddy simulation of a neutrally stratifi ed boundary layer: A
comparison of four computer codes. Q. J. R. Meteorol. Soc. 120: 1457–1484.
Boffetta, G. and I.M. Sokolov. 2002. Relative dispersion in fully developed turbulence: The
Richardson’s law and intermittency corrections. Phys. Rev. Lett. 88: 494–501
Boffetta, G., A. Celani, M. Cencini, G. Lacorata, and A. Vulpiani. 2000. Non Asymptotic
properties of transport and mixing, Chaos 10: 1–9.
Deardorff, J.W. 1970. Numerical simulation of turbulent channel fl ow at large Reynolds
number. J. Fluid Mech. 41: 452–480.
Deardorff, J.W. 1972. Numerical investigation of neutral and unstable planetary boundary
layers. J. Atmos. Soc., 29: 91–115.
Forester, C.K. 1979. Higher order monotonic convective difference schemes. J. Comput. Phys.
23: 1–22.
Fox, D.G. and S.A. Orszag. 1973. Pseudo-spectral approximation of two-dimensional turbulence. J. Comput. Phys. 11: 612–619.
Gioia, G., G. Lacorata, E.P. Marques Filho, A. Mazzino, and U. Rizza. 2004. The Richardson’s
law in large-eddy simulations of boundary layer fl ows. Bound. Layer Meteorol. 113:
187–199.
© 2010 by Taylor and Francis Group, LLC