Atmospheric Chemistry and Physics
www.atmos-chem-phys.net
1680-7316
1680-7324
8
6
2008
10.5194/acp-8-1713-2008
http://www.atmos-chem-phys.net/8/1713/2008/
http://www.atmos-chem-phys.net/8/1713/2008/acp-8-1713-2008.html
http://www.atmos-chem-phys.net/8/1713/2008/acp-8-1713-2008.pdf
1713
1721
2008-03-25
Turbulence dissipation rate derivation for meandering occurrences in a stable planetary boundary layer
G. A. Degrazia
degrazia@ccne.ufsm.br
A. Goulart
J. Costa Carvalho
C. R. P. Szinvelski
L. Buligon
A. Ucker Timm
Departamento de Física, Universidade Federal de Santa Maria, Santa Maria, RS, Brazil
Centro de Tecnologia de Alegrete, UNIPAMPA/UFSM, Alegrete, RS, Brazil
Faculdade de Meteorologia, Universidade Federal de Pelotas, Pelotas, RS, Brazil
A new formulation for the turbulence dissipation rate ε
occurring in meandering conditions has been presented. The derivation
consists of a MacLaurin series expansion of a lateral dispersion parameter
that represents cases in which turbulence and oscillatory movements
associated to the meandering events coexist. The new formulation presents
the identical physical premises contained in the classical and largely used
one, but the new formulation derived from meandering situations is expressed
in terms of the loop parameter <I>m</I> that controls the absolute value of the
negative lobe in the meandering autocorrelation function. Therefore, the <I>m</I>
magnitude regulates the turbulence dissipation rate. This dissipation rate
decreases for cases in which turbulence and low frequency horizontal wind
oscillations coexist and increases for a fully developed turbulence.
Furthermore, a statistical comparison to observed concentration data shows
that the alternative relation for the turbulent dissipation rate occurring
in situations of meandering enhanced dispersion is suitable for applications
in Lagrangian Stochastic dispersion models.
Anfossi, D., Ferrero, E., Sacchetti, D., and Trini Castelli, S.: Comparison among empirical probability density functions of the vertical velocity in the surface layer based on higher order correlations, Bound.-Lay. Meteorol., 82, 193–218, 1997.
Anfossi, D., Oettl, D., Degrazia, G. A., and Goulart, A.: An analysis of sonic anemomenter observations in low wind speed conditions, Bound.-Lay. Meteorol., 1(114), 179–203, 2005.
Brusasca, G., Tinarelli, G., and Anfossi, D.: Particle model simulation of diffusion in low wind speed stable conditions, Atmos. Environ., 26a, 707–723, 1992.
Carvalho, J. C., Nichimura, E. R., Vilhena, M. T. M. B., Moreira, D. M., and Degrazia, G. A.: An iterative langevin solution for contaminant dispersion simulation using the Gram-Charlier PDF, Environ. Mod. And Soft., 20(3), 285–289, 2005.
Carvalho, J. C. and Vilhena, M. T.: Pollutant dispersion simulation for low wind speed condition by the ils method, Atmos. Environ., 39, 6282–6288, 2005.
Chiba, O.: Stability dependence of the vertical wind velocity skewness in the atmospheric surface layer, J. Meteor. Soc. Japan, 56, 140–142, 1978.
Degrazia, G. A., Moraes, O. L. L., and Oliveira, A. P.: An Analytical method to evaluate mixing length scales for the planetary boundary layer, J. Appl. Meteor., 35, 974–977, 1996.
Degrazia, G. A., Acevedo, O. C., Carvalho, J. C., Goulart, A. G., Moraes, O. L. L., Campos Velho, H. F., and Moreira, D. M.: On the universality of the dissipation rate functional form and of autocorrelation function exponential form, Atmos. Environ., 39, 1917–1924, 2005.
Ferrero, E. and Anfossi, D.: Comparison of PDFs, closures schemes and turbulence parameterizations in Lagrangian Stochastic Models, Int. J. Environ. Pollut., 9, 384–410, 1998.
Frenkiel, F. N.: Turbulent diffusion: Mean concentration distribution in a flow field of homogeneous turbulence, Adv. Appl. Mech., 3, 61–107, 1953.
Goulart, A. G. O., Degrazia, G. A., Acevedo, O. C., and Anfossi, D.: Theoretical considerations of meandering winds in simplified conditions, Bound.-Lay. Meteorol., 125, 279–287, 2007.
Hanna, S. R.: Confidence limit for air quality models as estimated by bootstrap and jacknife resampling methods, Atmos. Environ., 23, 1385–1395, 1989.
Hinze, J. O.: Turbulence, MacGraw-Hill, New York, 790 pp, 1975.
Holton, J. R.: An Introduction to Dynamic Meteorology, Elsevier Academic Press, 535 pp., 2004.
Kendall, M. and Stuart, A.: The advanced theory of statistics, MacMillan, New York, 1977.
Kolmogorov, A. N.: The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers, Dokl. Akad. Nauk. SSSR, 30, 301–305, 1941.
Luhar, A. K. and Britter, R. E.: A random walk model for dispersion in inhomogeneous turbulence in a convective boundary layer, Atmos. Environ., 9, 1911–1924, 1989.
Manomaiphiboon, K. and Russel, A. G.: Evaluation of some proposed forms of Lagrangian velocity correlation coefficient, Int. J. Heat Fluid Flow, 24, 109–712, 2003.
Murgatroyd, R. J.: Estimations from geostrophic trajectories of horizontal diffusivity in the mid-latitude troposphere and lower stratosphere, Q. J. Roy. Meteor. Soc., 95, 40–62, 1969.
Oettl, D., Goulart, A., Degrazia, G., and Anfossi, D.: A new hypothesis on meandering atmospheric flows in low wind speed condition, Atmos. Environ., 39, 1739–1748, 2005.
Pope, S. B.: Turbulent Flows, Cambridge University Press, Cambridge, UK, 2000.
Rodean, H. C.: Stochastic Lagrangian models of turbulent diffusion, American Meteorological Society, Boston, 84 pp, 1996.
Sagendorf, J. F. and Dickson, C. R.: Diffusion under low wind-speed, inversion conditions, US National Oceanic and Atmospheric Administration Tech. Memorandum ERL ARL-52, 1974.
Sawford, B. L.: Reynolds number effects in Langragian stochastic models of turbulent dispersion, Phys. Fluids, A3, 1577–1586, 1991.
Sharan, M. and Yadav, A. K.: Simulation of experiments under light wind, stable conditions by a variable K-theory model, Atmos. Environ., 32, 3481–3492, 1998.
Stull, R. B.: An Introduction to Boundary Layer Meteorology, Kluver Academic Publishers, Dordrecht, Boston 666 pp, 1988.
Taylor, G. I.: Diffusion by continuous movements, Proc. London Math. Soc., 20, 196–211, 1921.
Tennekes, H.: The exponential Lagrangian correlation function and turbulent diffusion in the inertial subrange, Atmos. Environ., 12, 1565–1567, 1979.
Tennekes, H.: Similarity relation, scaling laws and spectral dynamics, in: Atmospheric Turbulence and Air Pollution Modeling, edited by: Nieuwstadt, F. T. M. and Van Dop, H., Reidel, Dordrecht, 37–68, 1982.
Thomson, D. J.: Criteria for the selection of stochastic models of particles trajectories in turbulent flows, J. Fluid Mech., 180, 611–615, 1987.
Yeung, P. K.: Lagrangian investigation of turbulence, Ann. Rev. Fluid Mech., 34, 115–142, 2002.
Wilson, J. D. and Sawford, B. L.: Review of Lagrangian stochastic models for trajectories in the turbulent atmosphere, Bound.-Lay. Meteorol., 78, 191–210, 1996.
Zannetti, P.: Air Pollution Modeling. Computational Mechanics Publitions, Southampton, 444 pp, 1990.
Zilitinkevich, S. S.: On the determination of the height of the Ekman boundary layer, Bound.-Lay. Meteorol., 3, 141–145, 1972.