B. A. Kader’s research while affiliated with Moscow Institute of Physics and Technology and other places

The turbulent structure of velocity and temperature fields in moving equilibrium retarded boundary layers is analyzed. Most attention is given to ‘the gradient sublayer’, where, according to Ginevskii and Solodkin [Prikl. Mat. Mech. (Appl. Math. Mech.) 22, 819–825 (1958)], Stratford [J. Fluid Mech.5, 1–16; 17–35 (1959)] and Perry et al. [J. Fluid Mech.25, 299–320 (1966)], the mean velocity and temperature profiles are described by the half-power and inverse half-power laws. Kader [Dokl. Akad. Nauk U.S.S.R.279, 323–327 (1984); Int. J. Heat Mass Trans.34, 2837–2857 (1991)] deduced formulas for spectra and cospectra of velocity components and temperature in the gradient sublayer for the mesoscale range of wave numbers k by dimensional analysis and then compared them with available experimental data. It is shown that accurate determination of velocity variances and Reynolds stresses requires taking into account the contribution of large-scale turbulent disturbances corresponding to small values of k. It is not so for determination of the temperature variance and vertical heat flux evaluation. An analysis of low wave number parts of velocity and temperature spectra and cospectra is given, and its results are used to determine the correlation functions of turbulent fluctuations in the gradient sublayer. The formulas for one-point second-order moments (variances 〈t2〉, 〈u2) and 〈v2〉, temperature flux 〈vt〉, and Reynolds stress 〈−uv〉) in the gradient sublayer of quasi-equilibrium flows are also derived and compared with the available data. Comparison of calculated and experimental spectra of non-equilibrium retarded flows uncovers disagreement in the mesoscale wave number part of the spectra for vertical velocity and Reynolds stress fluctuations. At the same time longitudinal fluctuation spectra and one-point variance 〈u2) prove to be less sensitive to non-equilibrium conditions.

Methods are studied which permit one to evaluate turbulent fluxes from the results of spectral measurements in turbulent laboratory flows and an unstable atmospheric surface layer. The well known dissipation method of flux measurements, which uses spectral data related to the inertial range, is reanalyzed. New theoretical ideas and the latest experimental data are used to specify this method in cases of moderately and very strongly unstable thermal stratifications.Moreover, it is also explained how to estimate momentum and heat fluxes from data in the low frequency parts of the velocity and temperature spectra in the low frequency ranges beyond the lower limit of the inertial range. This permits one to estimate fluxes using rather simple and cheap instruments (e.g., Pilot-tubes and thermocouples in laboratory flows or cup anemometers and crude resistance thermometers in meteorological studies). The equations for flux determination are based in such cases on the recent models by Kader (1987, 1988) and Kader and Yaglom (1990, 1991) of spectral shapes at mesoscale wave numbers; these models agree quite satisfactorily with many (though not all) data of direct spectral measurements. It is shown that estimated momentum and heat fluxes in the laboratory and in an unstably stratified atmospheric surface layer obtained by the method suggested in this paper agree satisfactorily with direct flux measurements.

Dimensional analysis and the asymptotic expansion method are used to investigate the structure of a scalar field in moving-equilibrium boundary layers with longitudinal pressure gradients. The available experimental data on temperature profiles in decelerating wall flows make it possible to determine universal constants and functions entering into the theoretical relationships and to obtain interpolation formulas describing the mean temperature field. Assuming that an overlap layer exists, where both the defect law and gradient-sublayer law are valid, the universal heat and mass transfer law can be obtained. The numerical coefficients of this law are estimated for decelerating pressure-gradient flows. The forms of some statistical characteristics of temperature fluctuations in the gradient sublayer are found by dimensional analysis and compared with the available experimental data.

The results of an experiment carried out in the summer of 1988 in the forest-steppe region of the USSR are given. The aim of the experiment was to study turbulent exchange between the atmosphere and a non-homogeneous underlying surface consisting of a patchwork quilt of agricultural lands sown with different crops (hereafter called chessboard-type inhomogeneities). Simultaneous measurements of turbulent fluxes of heat, momentum and humidity by the eddy-correlation methods and also the measurements of the mean wind velocity and temperature are described. The values of turbulent fluxes calculated from the profile measurements are in good agreement with those obtained from the eddy-correlation measurements. Thus it may be concluded that the universal functions of Monin-Obukhov similarity theory (determined from measurements over a flat and homogeneous underlying surface) pertain also to a non-homogeneous (chessboard-type) underlying surface.

The earliest results concerning the turbulence structure in a turbulent boundary layer with very unstable thermal stratification are due to Prandtl (1932). These results were developed further and made more precise by Obukhov (1946, 1960), Monin & Obukhov (1954) and Priestley (1954, 1955, 1956, 1960). All of these authors dealt with a surface layer of the Earth's atmosphere on hot summer days. Such a layer is the most easily accessible example of an unstably stratified boundary layer and it will be the main concern in this paper too. The theoretical predictions by the above-mentioned authors seemed at first to be confirmed by the available experimental data but in the late 1960s it became clear that at least some of the predictions disagreed strongly with the experimental information.

The longitudinal (i.e., in the direction of the mean wind) spectra and cospectra of wind components and temperature fluctuations in the atmospheric surface layer during neutral conditions were carefully investigated by Kader (1984, 1987) for a broad range of wave numbers which included wavelengths far beyond the large-scale limit of the inertial subrange. At the same time, some direct measurements of spatial correlation functions of the longitudinal wind component and temperature were performed by Zubkovskii and Fedorov (1986) and Zubkovskii and Sushko (1987). Section 2 of the present paper gives a review of the available results on longitudinal spectra and cospectra of wind velocity and temperature fluctuations in neutral stratification and examines the consequences of these results related to the longitudinal autocorrelation and symmetrized cross-correlation functions of surface-layer turbulence. In Section 3 it is shown that the correlation equations of Section 2 agree satisfactorily with some recent measurements of the longitudinal correlation functions in the range of distances from 3 m to 100 m. Some measurements of the lateral correlation functions of atmospheric turbulence are also presented in Section 3. It is shown that these measurements lead to some predictions concerning the never-measured lateral space spectra of surface-layer turbulence.

The main results of the International Turbulence Comparison Experiment (Tsimlyansk, U.S.S.R., June–July 1981) are presented. Groups from G.D.R., Poland, U.S.S.R., and Czechoslovakia took part in the experiment, while Bulgarian researchers were present as observers. A comparison of in situ measurements (by acoustic anemometers, thermoanemometers, and resistance thermometers) among themselves and with remote soundings (by sodars) was made. Simultaneous measurements of turbulent fluctuation characteristics and of wind velocity and temperature profiles were performed by different instruments. The results and temperature profiles were performed by different instruments. The results of these measurements were used to estimate the comparative accuracy of various models proposed for the evaluation of turbulent fluxes from profile data.

The turbulence characteristics of very small (compared with the exterior scale of the flow) vortices in a developed turbulent boundary layer can be described with good accuracy by the Kolmogorov—Obukhov theory of locally isotropic turbulence. However, it does not apply to turbulent disturbances of large scale, for which the pulsations of the velocity and the temperature cannot be assumed to be isotropic. The aim of the present paper is to investigate the spectral and correlation characteristics of the turbulent field of the velocities and temperatures in the logarithmic sublayer of a gradientless flow for scales appreciably less than the boundary layer thickness but greater than the value below which the assumption of local isotropy holds. Attention is drawn to the part played by the interior turbulence scale (under the considered conditions, the distance to the wall), which distinguishes the hyperbolic law of variation of the spectrum characteristic of anisotropic pulsations of the velocity and the temperature and the five-thirds power law for isotropic vortices. Comparison of the derived relations with the available experimental data makes it possible not only to verify the validity of these laws but also to determine the values of the universal constants in them. The stability of the obtained laws with respect to disturbances localized in the wall region (roughness, blowing and suction, polymer additives, etc.) is discussed.