Abstract
From measured one-dimensional spectra of velocity and temperature variance, the universal functions of the Monin-Obukhov similarity theory are calculated for the range −2 z/L + 2. The calculations show good agreement with observations with the exception of a range −1 z/L 0 in which the function Φ m , i.e., the nondimensional mean shear, is overestimated. This overestimation is shown to be caused by neglecting the spectral divergence of a vertical transport of turbulent kinetic energy. The integral of the spectral divergence over the entire wave number space is suggested to be negligibly small in comparison with production and dissipation of turbulent kinetic energy.
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Abbreviations
- a,b,c:
-
contants (see Equations (–4))
- Ci :
-
constants i=u, v, w, θ (see Equation (5)
- kme,kmT :
-
peak wave numbers of 3-d moel spectra of turbulent kinetic energy and of temperature variance, respectively
- kmi :
-
peak wave numbers of 1-d spectra of velocity components i=u, v, w and of temperature fluctuations i=θ
- ksb, kc :
-
characteristics wave numbers of energy-feeding by mechanical effects being modified by mean buoyancy, and of convective energy feeding, respectively
- L:
-
Monin-Obukhov length
- % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% Gabeivayaaraaaaa!3C5B!\[{\rm{\bar T}}\]:
-
difference of mean temperature and mean potential temperature
- T*:
-
Monin-Obukhov temperature scale
- Ū:
-
velocity of mean flow in positive x-direction
- u*:
-
friction velocity
- u, v, w:
-
components of velocity fluctuations
- z:
-
height above ground
- κ:
-
von Kármanán constant
- θ:
-
temperature fluctuation
- φm :
-
nondimensional mean shear
- φH :
-
nondimensional mean temperature gradient
- φɛ :
-
nondimensional rate of lolecular dissipation φ of turbulent kinetic energy
- φD :
-
nondimensional divergence of vertical transports of turbulent linetic energy
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Claussen, M. Estimation of the Monin-Obukhov similarity functions from a spectral model. Boundary-Layer Meteorol 33, 233–243 (1985). https://doi.org/10.1007/BF00052057
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DOI: https://doi.org/10.1007/BF00052057