Boundary-Layer Meteorology

, Volume 153, Issue 1, pp 19–41 | Cite as

Effects of Temporal Discretization on Turbulence Statistics and Spectra in Numerically Simulated Convective Boundary Layers

  • Jeremy A. Gibbs
  • Evgeni Fedorovich


Six state-of-the-art large-eddy simulation codes were compared in Fedorovich et al. (Preprints, 16th American Meteorological Society Symposium on Boundary Layers and Turbulence, 2004b) for three airflow configurations in order to better understand the effect of wind shear on entrainment dynamics in the convective boundary layer CBL). One such code was the University of Oklahoma large-eddy simulation (LES) code, which at the time employed a second-order leapfrog time-advancement scheme with the Asselin filter. In subsequent years, the code has been updated to use a third-order Runge–Kutta (RK3) time-advancement scheme. This study investigates what effect the upgrade from the leapfrog scheme to RK3 scheme has on turbulence statistics in the CBL differently affected by mean wind shear, also in relation to predictions by other LES codes that participated in the considered comparison exercise. In addition, the effect of changing the Courant number within the RK3 scheme is investigated by invoking the turbulence spectral analysis. Results indicate that low-order flow statistics obtained with the RK3 scheme generally match their counterparts from simulations with the leapfrog scheme rather closely. CBL growth rates due to entrainment in the shear-free case were also similar using both timestepping schemes. It was found, however, that care should be given to the choice of the Courant number value when running LES with the RK3 scheme in the sheared CBL setting. The advantages of the largest possible (based on the stability criterion) Courant number were negated by degrading the energy distribution across the turbulence spectrum. While mean profiles and low-order turbulence statistics were largely unaffected, the entrainment rate was over-predicted compared to that reported in the original code-comparison study.


Convective boundary layer Entrainment Large-eddy simulation Wind shear 



The authors wish to thank Alan Shapiro, Louis Wicker, and Lance Leslie for helpful conversations related to the scope of this paper.


  1. Asselin R (1972) Frequency filter for time integrations. Mon Weather Rev 100:487–490CrossRefGoogle Scholar
  2. Deardorff JW (1980) Stratocumulus-capped mixed layers derived from a three-dimensional model. Boundary-Layer Meteorol 18:495–527Google Scholar
  3. Durran DR (2010) Numerical methods for fluid dynamics: with applications to geophysics, 2nd edn. Springer, Berlin, 516 ppGoogle Scholar
  4. Fedorovich E, Conzemius R, Mironov D (2004a) Convective entrainment into a shear-free linearly stratified atmosphere: bulk models reevaluated through large eddy simulations. J Atmos Sci 61:281–295CrossRefGoogle Scholar
  5. Fedorovich E, Conzemius R, Esau I, Chow FK, Lewellen D, Moeng C-H Pino D, Sullivan P, de Arellano JVG ( 2004b) Entrainment into sheared convective boundary layers as predicted by different large eddy simulation codes. In: Preprints, 16th symposium on boundary layers and turbulence. Portland, MaineGoogle Scholar
  6. Fedorovich E, Nieuwstadt FTM, Kaiser R (2001) Numerical and laboratory study of horizontally evolving convective boundary layer. Part I: transition regimes and development of the mixed layer. J Atmos Sci 58:70–86CrossRefGoogle Scholar
  7. Kaiser R, Fedorovich E (1998) Turbulence spectra and dissipation rates in a wind tunnel model of the atmospheric convective boundary layer. J Atmos Sci 55:580–594CrossRefGoogle Scholar
  8. Nieuwstadt FTM (1990) Direct and large-eddy simulation of free convection. Proceedings of Ninth International Heat Transfer Conference. Jerusalem, Israel, pp 37–47Google Scholar
  9. Shapiro A, Fedorovich E (2008) Coriolis effects in homogeneous and inhomogeneous katabatic flows. Q J R Meteorol Soc 134:353–370CrossRefGoogle Scholar
  10. Skamarock WC (2004) Evaluating mesoscale NWP models using kinetic energy spectra. Mon Weather Rev 132:3019–3032CrossRefGoogle Scholar
  11. Sullivan PP, McWilliams JC, Moeng C-H (1996) A grid nesting method for large-eddy simulation of planetary boundary-layer flows. Boundary-Layer Meteorol 80:167–202CrossRefGoogle Scholar
  12. Sullivan PP, Moeng C-H, Stevens B, Lenschow DH, Mayor SD (1998) Structure of the entrainment zone capping the convective atmospheric boundary layer. J Atmos Sci 55:3042–3064CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.School of MeteorologyUniversity of OklahomaNormanUSA

Personalised recommendations