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Estimation of the Lagrangian Velocity Structure Function Constant C0 by Large-Eddy Simulation

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Abstract

The inertial subrange Kolmogorov constant C 0, which determines the effective turbulent diffusion in velocity space, plays an important role in the Lagrangian modelling of pollutants. A wide range of values of the constant are found in the literature, most of them determined at low Reynolds number and/or under different assumptions. Here we estimate the constant C 0 by tracking an ensemble of Lagrangian particles in a planetary boundary layer simulated with a large-eddy simulation model and analysing the Lagrangian velocity structure function in the inertial subrange. The advantage of this technique is that it easily allows Reynolds numbers to be achieved typical of convective turbulent flows. Our estimates of C 0 is C 0=4.3±0.3 consistent with values found in the literature

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References

  • Anfossi D., Degrazia G.A., Ferrero E., Gryning S.E., Morselli M.G., and Trini Castelli S. (2000). ‘Estimation of the Lagrangian Structure Function Constant C0 from Surface Layer Wind Data’. Boundary-Layer Meteorol 95:249–270

    Article  Google Scholar 

  • Antonelli M., Mazzino A., and Rizza U. (2003). ‘Statistics of Temperature Fluctuations in a Buoyancy Dominated Boundary-Layer Flow Simulated by a Large-Eddy Simulation Model’. J. Atmos. Sci 60:215–224

    Article  Google Scholar 

  • Armenio V., Piomelli U., and Fiorotto V. (1999). ‘Effect of Subgrid Scales on Particle Motion’. Phys. Fluids 11:3030–3042

    Article  Google Scholar 

  • Biferale L., Boffetta G., Celani A., Lanotte A., and Toschi F. (2005). ‘Particle Trapping in Three-dimensional Fully Developed Turbulence’. Phys. Fluids 17:021701/1–021701/4

    Google Scholar 

  • Degrazia G.A. and Anfossi D. (1998). ‘Estimation of the Kolmogorov Constant C 0 from Classical Statistical Diffusion Theory’. Atmos. Environ 32:3611–3614

    Article  Google Scholar 

  • Du S., Wilson J.D., and Yee E. (1994). ‘Probability Density Functions for Velocity in the Convective Boundary Layer and Implied Trajectory Models’. Atmos. Environ 28:1211–1217

    Article  Google Scholar 

  • Du S., Sawford B.L., Wilson J.D., and Wilson D.J. (1995). ‘Estimation of the Kolmogorov Constant for the Lagrangian Structure Function, Using a Second-Order Lagrangian Model of Grid Turbulence’. Phys. Fluids 7:3083–3090

    Article  Google Scholar 

  • Ferrero E. and Anfossi D. (1998). ‘Sensitivity Analysis of Lagrangian Stochastic Models for CBL with Different PDF’s and Turbulence Parameterizations’. In: Gryning S.E. and Chaumerliac N (eds). Air Pollution Modelling and Its Applications XI Vol 22. Plenum Press, New York, pp. 267–273

    Google Scholar 

  • Gioia G., Lacorata G., Marques Filho E.P., Mazzino A., and Rizza U. (2004). ‘Richardson’s Law in Large-Eddy Simulations of Boundary Layer Flows’. Boundary-Layer Meteorol 113:187–199

    Article  Google Scholar 

  • Hanna S.R. (1981). ‘Lagrangian and Eulerian Time-Scale in the Daytime Boundary Layer’. J. Appl. Meteorol 20:242–249

    Article  Google Scholar 

  • Lien R.C., and D’Asaro E.A. (2002). ‘The Kolmogorov Constant for the Lagrangian Velocity Spectrum and Structure Function’. Phys. Fluids 14:4456–4459

    Article  Google Scholar 

  • Luhar A.K. and Britter R.E. (1989). ‘A Random Walk Model for Dispersion in Inhomogeneous Turbulence in a Convective Boundary Layer’. Atmos. Environ 23:1191–1924

    Google Scholar 

  • Moeng C.-H. (1984). ‘A Large-Eddy-Simulation Model for the Study of Planetary Boundary-Layer Turbulence’. J. Atmos. Sci 41:2052–2062

    Article  Google Scholar 

  • Moeng C.-H. and Sullivan P.P. (1994). ‘A Comparison of Shear and Buoyancy Driven Planetary Boundary Layer Flows’. J. Atmos. Sci 51:999–1021

    Article  Google Scholar 

  • Monin A.S. and Yaglom A.M. (1975). Statistical Fluid Mechanics: Mechanics of Turbulence. MIT Press, Mass, Vol. 2, 874 pp

    Google Scholar 

  • Mordant N., Metz P., Michel O., and Pinton J.-F. (2001). ‘Measurement of Lagrangian Velocity in Fully Developed Turbulence’. Phys. Rev. Lett 21:214501/1 – 214501/4

    Google Scholar 

  • Leonard A. (1974). ‘Energy Cascade in Large Eddy Simulation of Turbulent Flow’. Adv. Geophys 18A:237–248

    Google Scholar 

  • Lilly, D. K.: 1967. ‘The Representation of Small-scale Turbulence in Numerical Simulation Experiments’, in Proc. IBM Scientific Computing Symp. on Environmental Science, Thomas J. Watson Research Center, Yorktown Heights, pp. 195–210

  • Press W.H., Teukolsky S.A., Vettering W.T., and Flannery B.P. (1992). Numerical Recipes in FORTRAN: the Art of Scientific Computing. Cambridge University Press, U.K., 963 pp.

    Google Scholar 

  • Pope S.B. (1987). ‘Consistency Conditions for Random Walk Models of Turbulent Dispersion’. Phys. Fluids 30:2374–2379

    Article  Google Scholar 

  • Rotach M.W., Gryning S.E., and Tassone C. (1996). ‘A Two-dimensional Lagrangian Stochastic Dispersion Model for Daytime Conditions’. Quart. J. Roy. Meteorol. Soc 122(530):367–389 Part B

    Article  Google Scholar 

  • Sawford, B. L. and Guest, F. M.: 1988, ‘Uniqueness and Universality of Lagrangian Stochastic Models of Turbulent Dispersion’, in 8th Symposium on Turbulence and Diffusion, Amer. Meteorol. Soc., San Diego, CA, pp. 96–99.

  • Sawford B.L. and Yeung P.K. (2001). ‘Lagrangian Statistics in Uniform Shear Flow: DNS and Lagrangian Stochastic Models’. Phys. Fluids 13:2627–2634

    Article  Google Scholar 

  • Smagorinsky J. (1963). ‘General Circulation Experiments with the Primitive Equations. I. The Basic Experiment’. Mon. Wea. Rev 91:99–164

    Article  Google Scholar 

  • Sullivan P.P., Mc Williams J.C., and Moeng C.H. (1994). ‘A Subgrid-scale Model for Large-Eddy Simulation of Planetary Boundary Layer Flows’. Boundary-Layer Meteorol 71:247–276

    Article  Google Scholar 

  • Taylor G.I. (1921). ‘Diffusion by Continuous Movements’. Proc. London Math. Soc., Ser. 2 20:196–211

    Article  Google Scholar 

  • Tennekes H. and Lumley J.L. (1972). A First Course in Turbulence. MIT Press, Mass, 300 pp

    Google Scholar 

  • Thomson D.J. (1987). ‘Criteria for the Selection of Stochastic Models of Particle Trajectories in Turbulent Flows’. J. Fluid Mech 180:529–556

    Article  Google Scholar 

  • Townsend A.A. (1956). The Structure of Turbulent Shear Flow. Cambridge University Press, Cambridge, 130 pp

    Google Scholar 

  • Weil J.C. (1990). ‘A Diagnosis of the Asymmetry in Top-down and Bottom-up Diffusion using a Lagrangian Stochastic Model’. J. Atmos. Sci 47:501–515

    Article  Google Scholar 

  • Weil J.C., Sullivan P.P., and Moeng C.H. (2004). ‘The Use of Large-Eddy Simulations in Lagrangian Particle Dispersion Models’. J. Atmos. Sci 61:2877–2887

    Article  Google Scholar 

  • Wilson J.D. and Sawford B.L. (1996). ‘Review of Lagrangian Stochastic Models for Trajectories in the Turbulent Atmosphere’. Boundary-Layer Meteorol 78:191–210

    Article  Google Scholar 

  • Wilson J.D., Legg B.J., and Thomson D.J. (1983). ‘Calculation of Particle Trajectories in the Presence of a Gradient in Turbulent-Velocity Variance’. Boundary-Layer Meteorol 27:163–169

    Article  Google Scholar 

  • Wyngaard J.C. (1982). Boundary-Layer Modeling. In: Nieuwstadt F.T.M. and van Dop H (eds). Atmospheric Turbulence and Air pollution Modelling. Reidel, Dordrecht, pp. 69–106

    Google Scholar 

  • Yeung P.K. and Pope S.B. (1988). ‘An Algorithm for Tracking Fluid Particles in Numerical Simulations of Homogeneous Turbulence’. J. Comput. Phys 79:373–416

    Article  Google Scholar 

  • Yeung P.K. (2001). ‘Lagrangian Characteristics of Turbulence and Scalar Transport in Direct Numerical Simulations’. J. Fluid Mech 427:241–274

    Article  Google Scholar 

  • Yeung P.K. (2002). ‘Lagrangian Investigation of Turbulence’. Annu. Rev. Fluid Mech 34:115–142

    Article  Google Scholar 

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Correspondence to Umberto Rizza.

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Rizza, U., Mangia, C., Carvalho, J.C. et al. Estimation of the Lagrangian Velocity Structure Function Constant C0 by Large-Eddy Simulation. Boundary-Layer Meteorol 120, 25–37 (2006). https://doi.org/10.1007/s10546-005-9039-z

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