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Monin–Obukhov Similarity Functions for the Structure Parameters of Temperature and Humidity in the Unstable Surface Layer: Results from High-Resolution Large-Eddy Simulations

Björn MarongaInstitut für Meteorologie und Klimatologie, Leibniz Universität Hannover, Hannover, Germany

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Abstract

Large-eddy simulations (LESs) of free-convective to near-neutral boundary layers are used to investigate the surface-layer turbulence. The article focuses on the Monin–Obukhov similarity theory (MOST) relationships that relate the structure parameters of temperature and humidity to the surface fluxes of sensible and latent heat, respectively. Moreover, the applicability of local free convection (LFC) similarity scaling is studied. The LES data suggest that the MOST function for is universal. It is shown to be within the range of the functions proposed from measurement data. It is found that follows MOST if entrainment of dry air from the free atmosphere is sufficiently small. In this case the similarity functions for and are identical. If entrainment is significant, dissimilarity between the transport of sensible heat and moisture is observed and no longer follows MOST. In the free-convection limit the LFC similarity functions should collapse to universal constants. The LES data suggest values around 2.7, which is in agreement with the value proposed in the literature. As for MOST, the LFC similarity constant for becomes nonuniversal if entrainment of dry air is significant. It is shown that LFC scaling is applicable even if shear production of turbulence is moderately high.

Corresponding author address: Björn Maronga, Institut für Meteorologie und Klimatologie, Herrenhäuser Str. 2, 30419 Hannover, Germany. E-mail: maronga@muk.uni-hannover.de

Abstract

Large-eddy simulations (LESs) of free-convective to near-neutral boundary layers are used to investigate the surface-layer turbulence. The article focuses on the Monin–Obukhov similarity theory (MOST) relationships that relate the structure parameters of temperature and humidity to the surface fluxes of sensible and latent heat, respectively. Moreover, the applicability of local free convection (LFC) similarity scaling is studied. The LES data suggest that the MOST function for is universal. It is shown to be within the range of the functions proposed from measurement data. It is found that follows MOST if entrainment of dry air from the free atmosphere is sufficiently small. In this case the similarity functions for and are identical. If entrainment is significant, dissimilarity between the transport of sensible heat and moisture is observed and no longer follows MOST. In the free-convection limit the LFC similarity functions should collapse to universal constants. The LES data suggest values around 2.7, which is in agreement with the value proposed in the literature. As for MOST, the LFC similarity constant for becomes nonuniversal if entrainment of dry air is significant. It is shown that LFC scaling is applicable even if shear production of turbulence is moderately high.

Corresponding author address: Björn Maronga, Institut für Meteorologie und Klimatologie, Herrenhäuser Str. 2, 30419 Hannover, Germany. E-mail: maronga@muk.uni-hannover.de
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