Advanced Numerical Modeling of Turbulent Atmospheric Flows

  • Christian Kühnlein
  • Andreas Dörnbrack
  • Thomas Gerz
Part of the Research Topics in Aerospace book series (RTA)


The present chapter introduces the method of computational simulation to predict and study turbulent atmospheric flows. This includes a description of the fundamental approach to computational simulation and the practical implementation using the technique of large-eddy simulation. In addition, selected contributions from IPA scientists to computational model development and various examples for applications are given. These examples include homogeneous turbulence, convective boundary layers, heated forest canopy, buoyant thermals, and large-scale flows with baroclinic wave instability.


Direct Numerical Simulation Convective Boundary Layer Computational Simulation Internal Gravity Wave Atmospheric Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Clark T.L., Farley R.D.: Severe downslope windstorm calculations in two and three spatial dimensions using anelastic interactive grid nesting: a possible mechanism for gustiness. J. Atmos. Sci. 41, 329–350 (1984).  10.1175/1520-0469(1984)041<0329:SDWCIT>2.0.CO;2 Google Scholar
  2. Craig, G.C., Dörnbrack, A.: Entrainment in cumulus clouds:what resolution is cloud-resolving? J. Atmos. Sci. 65, 3978–3988 (2008). doi: 10.1175/2008JAS2613.1 ADSCrossRefGoogle Scholar
  3. Deardorff, J.W.: Three-dimensional numerical study of turbulence in an entraining mixed layer. Bound. Layer Meteor. 7, 199–226 (1974). doi: 10.1007/BF00227913 ADSGoogle Scholar
  4. Dörnbrack, A.: Turbulent mixing by breaking gravity waves. J. Fluid Mech. 375, 113–141 (1998)MathSciNetADSzbMATHCrossRefGoogle Scholar
  5. Gerz, T., Schumann, U.: A possible explanation of countergradient fluxes in homogeneous turbulence. Theor. Comput. Fluid Dyn. 8, 169–181 (1996). doi: 10.1007/BF00418056 zbMATHCrossRefGoogle Scholar
  6. Gerz, T., Schumann, U., Elghobashi, S.E.: Direct numerical simulation of stratified homogeneous turbulent shear flows. J. Fluid Mech. 200, 563–594 (1989). doi: 10.1017/S0022112089000765 ADSzbMATHCrossRefGoogle Scholar
  7. Geurts, B.J.: Elements of Direct and Large-Eddy Simulation. R.T. Edwards Inc., Flourtown (2003)Google Scholar
  8. Grinstein, F.F., Margolin, L.G., Rider, W.J. (Eds.): Implicit Large Eddy Simulation: Computing Turbulent Flow Dynamics. Cambridge University Press, New York (2007)Google Scholar
  9. Kolmogorov, A.: The local structure of turbulence in incompressible viscous fluid for very large Reynolds’ numbers. Akademiia Nauk SSSR Doklady 30, 301–305 (1941)ADSGoogle Scholar
  10. Kühnlein, C.: Solution-adaptive moving mesh solver for geophysical flows. Ph.D. thesis, Ludwig-Maximilians-Universität München (2011)Google Scholar
  11. Kühnlein, C., Smolarkiewicz, P.K., Dörnbrack, A.: Modelling atmospheric flows with adaptive moving meshes. J. Comput. Phys. 231(7), 2741–2763 (2012). doi: 10.1016/ MathSciNetADSzbMATHCrossRefGoogle Scholar
  12. Lilly, D.K.: The representation of small scale turbulence in numerical simulation experiments. IBM Sci. Comput. Symp. Environ. Sci. 195–210 (1967)Google Scholar
  13. Moeng, C.-H., Schumann, U.: Composite structure of plumes in stratus-topped boundary layers. J. Atmos. Sci. 48, 2280–2292 (1991). doi: 10.1175/1520-0469(1991)048<2280:CSOPIS>2.0.CO;2 Google Scholar
  14. Nieuwstadt, F.T.M., Mason, P.J., Moeng, C.H. et al.: Large-eddy simulation of the convective boundary layer—A comparison of four computer codes. Thin Solid Films 1, 1–4 (1991)Google Scholar
  15. Potter, D.: Computational Physics. Wiley, New York (1973)Google Scholar
  16. Prusa, J.M., Smolarkiewicz, P.K., Wyszogrodzki, A.A.: EULAG, a computational model for multiscale flows. Comput. Fluids 37, 1193–1207 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  17. Richardson, L.F.: Weather Prediction by Numerical Process. Cambridge University Press, Cambridge (1922)Google Scholar
  18. Schmidt, H., Schumann, U.: Coherent structure of the convective boundary layer derived from large-eddy simulations. J. Fluid Mech. 200, 511–562 (1989). doi: 10.1017/S0022112089000753. ADSzbMATHCrossRefGoogle Scholar
  19. Schröttle, J., Dörnbrack, A.: Turbulence structure in a diabatically heated forest canopy composed of fractal pythagoras trees. submitted to Theor. Comput. Fluid Dyn. Dec 2011 (2012)Google Scholar
  20. Schumann, U.: Subgrid scale model for finite difference simulations of turbulent flows in plane channels and annuli. J. Comput. Phys. 18, 376–404 (1975). doi: 10.1016/0021-9991(75)90093-5 MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. Schumann, U.: Subgrid length-scales for large-eddy simulation of stratified turbulence. Theor. Comput. Fluid Dyn. 2, 279–290 (1991). doi: 10.1007/BF00271468 zbMATHCrossRefGoogle Scholar
  22. Schumann, U.: Stochastic backscatter of turbulence energy and scalar variance by random subgrid-scale fluxes. Proc. R. Soc. A. 451, 293–318 (1995). doi: 10.1098/rspa.1995.0126
  23. Schumann, U., Moeng, C.-H.: Plume budgets in clear and cloudy convective boundary layers. J. Atmos. Sci. 48, 1758–1770 (1991a). doi: 10.1175/1520-0469(1991)048<1758:PBICAC>2.0.CO;2
  24. Schumann, U., Moeng, C.-H.: Plume fluxes in clear and cloudy convective boundary layers. J. Atmos. Sci. 48, 1746–1757 (1991b). doi: 10.1175/1520-0469(1991)048<1746:PFICAC>2.0.CO;2
  25. Shaw, R.H., Schumann, U.: Large-eddy simulation of turbulent flow above and within a forest. Bound. Layer Meteor 61, 47–64 (1992). doi: 10.1007/BF02033994 ADSCrossRefGoogle Scholar
  26. Smagorinsky, J.: General circulation experiments with the primitive equations. Mon. Weather Rev. 91, 99–164 (1963). doi: 10.1175/1520-0493(1963)091<0099:GCEWTP>2.3.CO;2 Google Scholar
  27. Tuck, A.F.: Atmospheric turbulence: a molecular dynamics perspective. Oxford University Press, (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Christian Kühnlein
    • 1
  • Andreas Dörnbrack
    • 2
  • Thomas Gerz
    • 2
  1. 1.Ludwig-Maximilians-Universität München (LMU)Meteorological Institute Munich (MIM)MünchenGermany
  2. 2.DLR, Institute of Atmospheric Physics (IPA)OberpfaffenhofenGermany

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