Fluctuation spectra and variances in convective turbulent boundary layers: A reevaluation of old models

Abstract

Most of the existing theoretical models for statistical characteristics of turbulence in convective boundary layers are based on the similarity theory by Monin and Obukhov [Trudy Geofiz. Inst. Akad. Nauk SSSR 24(151), 163 (1954)], and its further refinements. A number of such models was recently reconsidered and partially compared with available data by Kader and Yaglom [J. Fluid Mech. 212, 637 (1990); Turbulence and Coherent Structures (Kluwer, Dordrecht, 1991), p. 387]. However, in these papers the data related to variances 〈u2〉=σ2u and 〈v2〉=σ2v of horizontal velocity components were not considered at all, and the data on horizontal velocity spectra Eu(k) and Ev(k) were used only for a restricted range of not too small wave numbers k. This is connected with findings by Kaimal et al. [Q. J. R. Meteorol. Soc. 98, 563 (1972)] and Panofsky et al. [Boundary-Layer Meteorol. 11, 355 (1977)], who showed that the Monin–Obukhov theory cannot be applied to velocity variance σ2u and σ2v and to spectra Eu(k) and Ev(k) in energy ranges of wave numbers. It is shown in this paper that a simple generalization of the traditional similarity theory, which takes into account the influence of large-scale organized structures, leads to new models of horizontal velocity variances and spectra, which describe the observed deviations of these characteristics from the predictions based on the Monin–Obukhov theory, and agree satisfactorily with the available data. The application of the same approach to the temperature spectrum and variance explains why the observed deviations of temperature spectrum in convective boundary layers from the Monin–Obukhov similarity does not lead to marked violations of the same similarity as applied to temperature variance 〈t2〉=σ2t.