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 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.     

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.     

Spatial coherence of temperature fluctuations in the atmospheric surface layer

Simultaneous temperature fluctuations have been measured along directions both parallel and orthogonal to the wind direction in the atmospheric surface layer. Ensemble-averaged temperature distributions associated with the ramp-like feature observed in instantaneous temperature traces indicate that the average duration of the ramp is approximately independent of height. Application of Davenport's geometric similarity of coherence of temperature fluctuations yields approximate estimates for the spatial extent of the structure characterized by the ramp. The longitudinal extent is approximately 12 times the vertical extent and 17 times the lateral extent.     

Geometric similarity for the temperature field in the unstable atmospheric surface layer

Davenport's geometric similarity is applied to the temperature field in the unstable atmospheric surface layer for displacements in all three orthogonal directions. The decay constants for lateral displacements are over 50 times as large as for vertical displacements. Such large lateral decay constants mean that the measurement of longitudinal constants will be very difficult.Some of the assumptions inherent in geometric similarity were not satisfied. Two regimes, plume scales and larger scales, having different decay constants, were observed. The possibility of a similar scale dependency of the decay constants for the wind field is discussed.     

Relationships between structure functions and temperature ramps in the atmospheric surface layer

The behaviour of odd-order structure functions of temperature in the atmospheric surface layer is consistent with the presence of a coherent structure characterised by temperature ramps. The use of a simple linear model for the ramp together with measurements of second-, third-, and fifth-order temperature structure functions yields estimates for the characteristic mean amplitude and repetition interval of ramps for stability conditions ranging from neutral to moderately unstable. Both amplitude and repetition interval compare favourably with values derived from observations of temperature traces obtained simultaneously at two heights in the surface layer.     

Non-dimensional wind and temperature profiles in the atmospheric surface layer: A re-evaluation

Previous results of non-dimensional wind and temperature profiles as functions of ( = z/L) show systematic deviations between different experiments. These discrepancies are generally believed not to reflect real differences but rather instrumental shortcomings. In particular, it is clear that flow distortion has not been adequately treated in most previous experiments. In the present paper, results are presented from a surface-layer field experiment where great care was taken to remove any effects from this kind of error and also to minimize other measuring errors. Data from about 90 30-min runs with turbulence measurements at three levels (3, 6, and 14 m) and simultaneous profile data have been analysed to yield information on flux-gradient relationships for wind and temperature.The flux measurements themselves show that the fluxes of momentum and sensible heat are constant within ± 7% on average for the entire 14 m layer in daytime conditions and when the stratification is slightly stable. For more stable conditions, the flux starts to decrease systematically somewhere in the layer 6 to 14 m. From a large body of data for near-neutral conditions (¦¦ 0.1), values are derived for von Kármán's constant: 0.40 ± 0.01 and for _h at neutrally, 0.95 ± 0.04. The range of uncertainty indicated here is meant to include statistical uncertainty as well as the effect of possible systematic errors.Data for _m and _h for an extended stability range (1 > > – 3) are presented. Several formulas for _m and _h appearing in the literature have been used in a comparative study. But first all the formulas have been modified in accordance with the following assumptions: = 0.40 and ( _h ) _{= 0} = 0.95; deviations from this result in the various studies are due to incomplete correction for flow distortion. After new corrections are introduced, the various formulas were compared with the present measurements and with each other. It is found that after this modification, the most generally used formulas for _m and _h for unstable conditions, i.e., those of Businger et al. (1971) and Dyer (1974) agree with each other to within ± 10% and with the present data. For stable conditions, the various formulas still disagree to some extent. The conclusion in relation to the present data is not as clear as for the unstable runs, because of increased scatter. It is, however, found that the modified curve of Businger et al. (1971) for _h fits the data well, whereas for _m , Dyer's (1974) curve appears to give slightly better agreement.     

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.     

Convective scaling of the average dissipation rate of temperature variance in the atmospheric surface layer

The flux of sensible heat from the land surface is related to the average rate of dissipation of temperature fluctuations in the atmospheric surface layer through the temperature variance budget equation. In many cases it is desirable to estimate the heat flux from measurement or inference of the dissipation rate. Here we study how the dissipation rate scales with atmospheric stability, using three inertial range methods to calculate the dissipation rate: power spectra, second order structure functions, and third order structure functions. Experimental data are analyzed from a pair of field experiments, during which turbulent fluctuations of velocity and temperature were measured over a broad range of neutral and unstable atmospheric flows. It is shown that the temperature dissipation rate scales with a single convective power law continuously from near-neutral to strongly unstable stratification. The dissipation scaling is found to nearly match production in the near-neutral region, but to be consistently lower than production in the more convective regimes. The convective scaling is shown to offer a simplified means of computing sensible heat flux from the dissipation rate of temperature variance.Also at Johns Hopkins University, Baltimore, MarylandAlso at Los Alamos National Laboratory, Los Alamos, New Mexico.     

One-year temperature records in the atmospheric surface layer above sea ice and open water

Temperature observations of three buoys drifting in the Weddell Sea for one year and covering the ice-water-ice cycle from July 1986 to July 1987 are presented. Significant differences between winter and summer are shown to be a consequence of the air-sea heat exchange being drastically modified by the sea ice cover. Over ice, prevailing variance is in the synoptic scale (periods 3 to 5 days) with amplitudes of 25 °C, whereas over water, the diurnal wave dominates with amplitudes of less than 1 °C.     

Third- and fourth-order mixed moments of turbulent velocity and temperature fluctuations in the atmospheric surface layer

Fourth-order mixed moments of velocity and temperature fluctuations, measured within the atmospheric surface layer, are compared with results obtained by assuming the quasi-Gaussian approximation. Standard deviations of the products uw, u and w(u and w are the longitudinal and vertical velocity fluctuations; is the temperature fluctuation) are in good agreement with those obtained using the quasi-Gaussian assumption. Good agreement is also obtained between measured and Gaussian estimates of fourth-order moments including all three fluctuations u, w, Schwarz inequalities, commonly used in the clipping approximation in turbulence modelling, are found to provide bounds for third-order moments of w, that are too conservative. More reasonable, tighter, bounds for these moments are given by inequalities obtained by Lumley.     

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.     

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.     

A study of temperature fluctuations in the atmospheric boundary layer

The spectral density of temperature fluctuations in the boundary layer has been studied in the range 0.2 to 2 Hz. It is shown that the temperature spectrum is strongly variable from one minute to the next and that the spectral slope tends to increase with the standard deviation of temperature fluctuations and with the stability of the medium. It is shown that C _T ² values computed from short time series (30 s) tend to be smaller than the C _T ² values computed from several minutes of record.Formerly at Laboratoire de Météorologie Dynamique du C.N.R.S. (Paris).     

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.     

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.