The Scaling Behaviour of a Turbulent Kinetic Energy Closure Model for Stably Stratified Conditions View Full Text


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Article Info

DATE

2007-12-19

AUTHORS

Peter Baas, Stephan R. de Roode, Geert Lenderink

ABSTRACT

We investigate the scaling behaviour of a turbulent kinetic energy (TKE) closure model for stably stratified conditions. The mixing length scale for stable stratification is proportional to the ratio of the square root of the TKE and the local Brunt–Väisälä frequency, which is a commonly applied formulation. We analyze the scaling behaviour of our model in terms of traditional Monin–Obukov Similarity Theory and local scaling. From the model equations, we derive expressions for the stable limit behaviour of the flux–gradient relations and other scaling quantities. It turns out that the scaling behaviour depends on only a few model parameters and that the results obey local scaling theory. The analytical findings are illustrated with model simulations for the second GABLS intercomparison study. We also investigate solutions for the case in which an empirical correction function is used to express the eddy diffusivity for momentum as a function of the Richardson number (i.e. an increasing turbulent Prandtl number with stability). In this case, it seems that for certain parameter combinations the model cannot generate a steady-state solution. At the same time, its scaling behaviour becomes unrealistic. This shows that the inclusion of empirical correction functions may have large and undesired consequences for the model behaviour. More... »

PAGES

17-36

References to SciGraph publications

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  • 2007-07-07. Similarity theory and calculation of turbulent fluxes at the surface for the stably stratified atmospheric boundary layer in BOUNDARY-LAYER METEOROLOGY
  • 2007-05-22. Energy- and flux-budget (EFB) turbulence closure model for stably stratified flows. Part I: steady-state, homogeneous regimes in BOUNDARY-LAYER METEOROLOGY
  • 2005-12-20. Revisiting the Local Scaling Hypothesis in Stably Stratified Atmospheric Boundary-Layer Turbulence: an Integration of Field and Laboratory Measurements with Large-Eddy Simulations in BOUNDARY-LAYER METEOROLOGY
  • 2007-02-24. The influence of nonstationarity on the turbulent flux–gradient relationship for stable stratification in BOUNDARY-LAYER METEOROLOGY
  • 2006-10-21. The role of surface heterogeneity in modelling the stable boundary layer in BOUNDARY-LAYER METEOROLOGY
  • 1988-01. Non-dimensional wind and temperature profiles in the atmospheric surface layer: A re-evaluation in BOUNDARY-LAYER METEOROLOGY
  • 2006-02. Preface: GEWEX Atmospheric Boundary-layer Study (GABLS) on Stable Boundary Layers in BOUNDARY-LAYER METEOROLOGY
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