Abstract
A model is described, in which the mean vertical wind profile and turbulence spectra at different heights are calculated for a turbulent boundary layer without thermal stratification. The model makes use of Heisenberg's formula for the transfer of turbulent energy and is based on the assumption of a constant shearing stress in that boundary layer. As a result, a logarithmic wind profile follows with 0.39 as the value of von Kármán's constant, which is — in this model — strongly related to the inertial subrange of the turbulent energy spectra and therefore to the Kolmogoroff constant.
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References
Batchelor, G. K.: 1960, The Theory of Homogeneous Turbulence, Cambridge University Press, Cambridge, England.
Ellison, T. H.: 1961, ‘The Universal Small-Scale Spectrum of Turbulence at High Reynolds Number’, in Mécanique de la turbulence, Colloque international, Marseilles, France.
Heisenberg, W.: 1948, ‘Zur statistischen Theorie der Turbulenz’, Z. Phys. 124, 628.
Roth, R.: 1969, ‘Ein primitives Modell zu Heisenbergs statistischer Theorie der Turbulenz’, Beitr. Phys. Atm. 42, 287.
Schlichting, H.: 1951, Grenzschichttheorie, Karlsruhe.
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Roth, R. On the existence of a relation between the Kolmogoroff and von Kármán constants. Boundary-Layer Meteorol 1, 131–136 (1970). https://doi.org/10.1007/BF00185734
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DOI: https://doi.org/10.1007/BF00185734