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.     

An aircraft study of turbulence dissipation rate and temperature structure function in the unstable marine atmospheric boundary layer

The dissipation rate of turbulent kinetic energy, , and the temperature structure function parameter, C _T ², have been measured over water from the near surface (Z = 3 m) to the top of the boundary layer. The near surface values of and C _T ² were used to calculate the velocity and temperature Monin-Obukhov scaling parameters u _* and T _*. The data collected during unstable lapse rates were used to evaluate the feasibility of extrapolating the values of and C _T ² as a function of height with empirical scaling formulae. The dissipation rate scaling formula of Wyngaard et al. (l971 a) gave a good fit to an average of the data for Z < 0.8 Z _i. In the surface layer the scaling formula of Wyngaard et al. (1971b) disagreed with the C _T ² values by as much as 50%. This disagreement is due to an unexpected reduction in the measured values of C _T ² forZ < 30 m. At this point it is not clear if the discrepancy is a unique property of the marine boundary layer or if it is simply some unknown instrumental or analytical problem. The mixed layer scaling results were similar to the overland results of Kaimal et al. (1976).     

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.     

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).     

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.     

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 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.     

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.