The observed relation between the Kolmogorov and von Karman constants in the surface boundary layer

In steady, neutrally-stratified flow over uniform terrain, the Kolmogorov constant for the one-dimensional spectrum in the inertial subrange (α ₁) and the von Karman constant of the logarithmic profile (k) are shown to be related by $$\alpha _1 k^{{4 \mathord{\left/ {\vphantom {4 3}} \right. \kern-\nulldelimiterspace} 3}} = \left[ {\frac{{\sum \phi }}{{0.555}}} \right]\left[ {\frac{{nz}}{{\bar U_z }}} \right]^{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-\nulldelimiterspace} 3}} \left[ {\frac{{\ln z_2 /z_1 }}{{\bar U_2 - \bar U_1 }}} \right]^2 \simeq 0.136,$$ , where the numerical value results from field measurements recorded in near-ideal conditions. This experimentally-observed Kolmogorov-von Karman ‘K-von K’ product is close to the value designated by a one-dimensional equivalent of the theoretical relation previously given by Roth (1970). More-over, it is in remarkably close agreement with new values of both constants independently proposed in recent years.     

On condensation and precipitation of atmospheric moisture in the surface layer

Presented are the computations of condensation and precipitation of atmospheric moisture at night depending on the diurnal variations of air temperature and air humidity. Used are the meteorological data for northern Dagestan. Determined is the contribution of the dew to the moistening of the soil. The examples of the exponential and lognormal distribution of droplets revealed that the use of the velocity of medium-size droplet underestimates the value of the moisture mass precipitated on the soil. A concept of the mean mass precipitation velocity is introduced, and the formulae are provided for determining the average mass of deposited condensate depending on humidity, the temperature drop, and size distribution of droplets. Posed is a new problem of diurnal condensate precipitation in the soil in summer and of technology of its increase.     

The Kolmogorov constant for carbon dioxide in the atmospheric surface layer over a paddy field

From measurements in the atmospheric surface layer over a paddy field, the Kolmogorov constants for CO₂ and longitudinal wind velocity were obtained. In this study, the nondimensional dissipation rate _nc = (1–16 _v )^-1/2 for CO₂ variance and = (1–16 _v )^-1/4 – _v for turbulent energy were used, assuming the equality of the local production term and the local dissipation term, and neglecting the divergence flux term in the budget equation. The value of the constant for CO₂ was consistent with recent determinations for temperature and humidity. The constant for longitudinal wind velocity showed good agreement with other recent observations.     

Turbulent dispersion in the atmospheric surface layer

By non-dimensionalizing a trajectory-simulation (TS) model of turbulent dispersion, it is shown that the dimensionless concentration z ₀cu_*/kQ (cu _*/kQ) due to a continuous line (area) source of strength Q in the atmospheric surface layer depends only on z/z ₀, x/z ₀, z ₀/L and z _s/z₀, where z _s is the source height. The TS model is used to tabulate concentration profiles due to ground-level line and area sources. Concentration profiles generated by the TS model for elevated sources are shown to be inconsistent with the Reciprocal Theorems of Smith (1957) and it is suggested that this is because the flux-mean gradient closure scheme inherent in the Reciprocal Theorem is invalid for an elevated source.     

Temperature structure in the atmospheric surface layer

Production, transport and dissipation terms in the temperature variance equation have been measured in the atmospheric surface layer. The transport term is, within the experimental uncertainty, negligible. The dissipation term, determined by assuming local isotropy, is approximately equal to production under near-neutral conditions. For moderately unstable conditions, the ratio of production to dissipation is 1.4. The resulting imbalance in the budget is attributed to the inequality between the three components of the dissipation term. The Kolmogorov constant for temperature is found to be about 0.8.     

Two-point coherence in the atmospheric surface layer

Two-point, one-dimensional coherence in horizontally homogeneous atmospheric turbulence is studied, both by experiment and analysis. Measurements are carried out using horizontally spaced sensors with the separation perpendicular to the mean velocity. Two-dimensional spectral models and three-dimensional inertial-range spectral tensors are used in the coherence calculations. The one-dimensional coherence for both velocity and scalar fluctuations is found to roll off at a wavenumber much smaller than we would expect from the classical notion of eddy correlation. This is a consequence of the cancellation of Fourier components aliased from the direction of the sensor separation into the streamwise direction. However, the coherence for the three velocity components behaves somewhat differently, reflecting the relative orientations of the velocity component, sensor separation and the mean velocity. These features are well predicted by the calculation. The analysis is also extended to calculate the two-point scalar-vertical velocity cospectrum and the results are in good agreement with our experimental data. The ratio of two- to one-point cospectra decreases at slightly larger wavenumber than the two-point scalar coherence does.     

On the analysis of wind wave-induced disturbances in the atmospheric turbulent surface layer

Simultaneous measurements of wind velocity, air humidity and sea surface wave-elevation fluctuations obtained on a platform in the open Caspian Sea are analyzed.It is shown that wave noises exist in the spectra and cospectra of the lower part of the atmospheric boundary layer, not only for the frequency of the main energy transporting component of the sea waves, but also in other parts of the spectra, at both lower and higher frequencies. The high frequencies are noncoherent with the sea waves and could be considered as measurement errors due to the existence of the waves. A method of elimination of the coherent wave noises from the spectra and cospectra is suggested and the effectiveness of its application is demonstrated.The essential difference between cases of developing and decaying wind waves is demonstrated.     

On the correlation between turbulent velocity and temperature derivatives in the atmospheric surface layer

Velocity and temperature derivatives were obtained at a height of 4 m in the atmospheric surface layer above land. With the assumption of local isotropy, these measurements are used to obtain some statistics of the turbulent energy and scalar dissipation fields. These statistics include the variances of the logarithms of the scalar and velocity dissipation fields and the correlation between these logarithms. When used in conjunction with the hypotheses for fluctuations in turbulent dissipation rates of Obukhov and Kolmogorov, the statistics suggest that the dependence of the flatness factor of temperature derivative on the turbulent Rynolds number R is not as large as that which had been previously reported in the literature. The experimental data indicate a R ^0.5 dependence for the kurtosis of the temperature derivative and a R ^0.15 variation for the strain rate-scalar dissipation correlation.     

Temperature and humidity spectra in the atmospheric surface layer

Temperature and humidity spectra have been measured at 3 and 12 m above the ground, together with profiles of wind, temperature and humidity, and flux measurements. Both temperature and humidity spectra appear to follow Monin-Obukov similarity as well as Kolmogorov's prediction for the inertial subrange. The standard deviations of temperature and humidity fluctuations support Monin-Obukov similarity and the predictions of local free convection. The spectral constants for the inertial subrange have been estimated as 0.8 for temperature and 0.6 for humidity.     

Microscale temperature fluctuations in the atmospheric surface layer

Microscale temperature fluctuations were measured at 2 m above a grassy surface. The temperature-derivative spectrum was in general agreement with earlier results but the bump at nondimensional wavenumbers higher than 0.02 was not as pronounced as has been observed. The Obukhov-Corrsin constant for the one-dimensional temperature spectrum was evaluated to be 0.92 ± 0.05, consistent with recent results. The effects of instability and the vertical variation of temperature variance and kinetic energy dissipation are postulated to explain some of the difference with other spectra.     

Spectra of temperature derivatives in the atmospheric surface layer

Measured spectra ofθ _x,θ _y,θ _z, the derivatives of temperature in streamwise, lateral and vertical directions, respectively, indicate that the spectral densities ofθ _z andθ _y are nearly similar but significantly different from the spectral density ofθ _x. The high-frequency parts of the three spectra satisfy, in a qualitative sense, local isotropy requirements. In the high-frequency end of the inertial subrange, the relative behaviour of spectra ofθ _x,θ _y andθ _z is also consistent with local isotropy.     

On similarity in the atmospheric boundary layer

A similarity theory for the atmospheric boundary layer is presented. The Monin-Obukhov similarity theory for the surface layer is a particular case of this new theory, for the case of z 0. Universal functions which are in agreement with empirical data are obtained for the stable and convective regimes.On leave from Institute of Environmental Engineering, Warsaw Technical University, 00653 Warsaw, Poland. Present address, Department of Geological and Geophysical Sciences, University of Wisconsin, Milwaukee, WI 53201 U.S.A.     

Gust and downward momentum transport in the atmospheric surface layer

The intermittent structure of the turbulent wind field in the atmospheric surface layer is investigated by conditional sampling methods. The results show that downward momentum can be transported efficiently during a peak gust. The horizontal structure of the gust is also revealed by observing the spatial structure of wind speed fluctuations from a network of 28 anemometers. The high wind region consists of a gust front with a sudden increase of wind speed at the front and a slow decrease to its rear. The development of the gust front is related closely to the momentum flux during the short time of passage of the gust.     

Streamwise heat flux budget in the atmospheric surface layer

Atmospheric surface-layer measurements of terms in the equation for the streamwise heat flux confirm previous results in both laboratory and atmosphere that the temperature-pressure gradient correlation acts as a sink, approximately equal in magnitude to the production term. The measured viscous dissipation term is independent of stability and represents less than 10% of the production term over the range of experimental stability conditions. Models for the temperature-pressure gradient correlation are compared with the measurements.     

Properties of spatial temperature derivatives in the atmospheric surface layer

A pair of parallel cold wires separated in either the vertical or lateral direction was used to obtain the three components _x, _y, _z of the temperature derivative in the streamwise, lateral and vertical directions, respectively. The average absolute skewness values of _x and _z are nonzero and approximately equal, while the skewness of _y is approximately zero. These results appear to be consistent with the presence of a large, three-dimensional organised structure in the surface layer. There is an apparent low-frequency contamination in the spectral density of _y and _z due mainly to small errors in estimating the sensitivity of the cold wires. The temperature derivatives were high-pass filtered, the filter being set to remove possible contributions from the large structure and to minimise low-frequency sensitivity contamination. The filtered rms ratios \~_x/\~_y and \~_x/\~_z were in the range 0.7 to 0.9, a result in qualitative agreement with that obtained in the laboratory boundary layer by Sreenivasan et al. (1977). The skewness of filtered _x or _z is negligible, consistent with local isotropy of small-scale temperature fluctuations and in support of the high wavenumber spectral isotropy discussed in Antonia and Chambers (1978).     

Characteristics of atmospheric turbulence in the surface layer over Antarctica

This paper presents meteorological measurements made during the antarctic summer period, on two 9 m and 3 m towers, on the rocky and ice shelf terrains of the Indian antarctic stations Maitri and Dakshin Gangotri, respectively. The measurements of fluctuations in temperature and wind speed made with relatively lesser precision instrumentation pertain to smaller wave numbers ~10^-2 m^-1 appropriate to outer scale L ₀ of the atmospheric turbulence spectrum. Autocorrelation analysis of the fluctuations in temperature and wind speed has been performed. A new autoregressive scheme has been developed to represent the computed autocorrelation functions by a Yule statistical model, and to estimate the correlation period T ₀ of the turbulent medium. Height profiles of outer scale L ₀ of turbulence may be given in terms of T ₀ and mean wind speed u. Further, the similarity theory of Monin-Obukhov has been used to compute height profiles of temperature structure parameter C _T ². At Maitri, values of L ₀ and C _T ² are higher between 03–22 h local time than between 22–03 h. Values of L ₀ and C _T ² are smaller over the ice shelf terrain of the Dakshin Gangotri station, compared to those over the rocky terrain of the Maitri station.     

A model of turbulence spectra in the atmospheric surface layer

The spectral equations of turbulent kinetic energy and temperature variance have been solved by using Onsager's energy cascade model and by extending Onsager's model to closure of terms that embody the interaction of turbulent and mean flow.The spectral model yields the following results: In a stably stratified shear flow, the peak wave numbers of the spectra of energy and temperature variance shift toward larger wave numbers as stability increases. In an unstably stratified flow, the peak wave numbers of energy spectra move toward smaller wave numbers as instability increases, whereas the opposite trend is observed for the peak wave numbers of temperature variance spectra. Hence, the peak wave numbers of temperature spectra show a discontinuity at the transition from stable to unstable stratification. At near neutral stratification, both spectra reveal a bimodal structure.The universal functions of the Monin-Obukhov similarity theory are predicted to behave as _m ~ _H ~ (- Z/L)^-1/3 in an extremely unstable stratification and as _m ~ _H ~ z/L in an extremely stable stratification. For a stably stratified flow, a constant turbulent Prandtl number is expected.