Horizontal coherence of wind fluctuations

The coherence for streamwise and cross-stream wind components is studied at four meteorological sites and compared with a representative wind-tunnel experiment. The coherence is approximated by a negative exponential in terms of a non-dimensional frequency, Δf and a decay parameter, a. Theoretical guidelines are developing to aid in identifying the pertinent variables affecting the decay parameters. These theoretical discussions indicate that for longitudinal separations, both the streamwise and cross-stream decay parameters are functions of roughness; the cross-stream decay parameter is a strong function of stability while the streamwise component is not. For lateral separations, it is found that both the streamwise and cross-stream decay parameters are functions of stability. Isopleths of the decay parameter are drawn on graphs with coordinates of angle and Richardson number for both the streamwise and cross-stream decay parameters of coherence. These empirical curves give an indication of the behavior of the decay parameters of coherence for a range of stabilities given by -0.9<Ri<0.08, and a range of angles between zero and ninety degrees. Department of Meteorology. Department of Aerospace Engineering.     

Taylor’s hypothesis and two-point coherence measurements

Experimentally obtained time coherence has traditionally been interpreted as streamwise one-dimensional spatial coherence through Taylor’s hypothesis. We calculate corrections to the highwavenumber part of the coherence to account for the errors caused by the deviation from Taylor’s hypothesis in high-intensity turbulent flows. The small-scale turbulence is assumed to be frozen and convected by a fluctuating convection velocity. Both Lumley’s two-term approximation and the Gaussian approximation are used in the calculations. In general, we find that the coherence for crossstream separations is significantly overestimated by the direct use of Taylor’s hypothesis, the error increasing with wavenumber; that for streamwise separations is underestimated. The analyses are compared with cross-stream coherence measurements in the atmospheric surface layer. Our results indicate that predictions from Lumley’s approximation yield better agreement with experimental data for cross-stream separations than those from the Gaussian model. Our study suggests that reliable measurement of two-point spatial coherence can be achieved only for scales not too small compared to the sensor separation.     

Horizontal, Two Point Coherence for Separations Greater Than the Measurement Height

Wind speed measurements from the test site at Rutherford Appleton Laboratory have been evaluated with respect to the spatial coherence function. The experimental arrangement provides coherence information for separation distances of 62, 80 and 102 m. These are at least three times greater than the measurement heights of 18 m and 18.7 m. Based on these experimental data and data published in the literature, different theoretical formulations are compared and a new, but simple, model for longitudinal and lateral coherence is proposed. At large separations the turbulent wind field is not isotropic, theoretical models to describe the coherence function for such distances are not available. The new model we propose builds on the classical exponential approach. It takes into account the influence of turbulence intensity and models the angular dependence of horizontal coherence. It is found that, for constant turbulence intensity, the lateral coherence decay becomes independent of the mean wind speed.     

On longitudinal spectral coherence

It is demonstrated that the longitudinal spectral coherence differs significantly from the transversal spectral coherence in its dependence on displacement and frequency. An expression for the longitudinal coherence is derived and it is shown how the scale of turbulence, the displacement between observation sites and the turbulence intensity influence the results. The limitations of the theory are discussed.     

On Longitudinal Spectral Coherence

It is demonstrated that the longitudinal spectral coherence differs significantly from the transversal spectral coherence in its dependence on displacement and frequency. An expression for the longitudinal coherence is derived and it is shown how the scale of turbulence, the displacement between observation sites and the turbulence intensity influence the results. The limitations of the theory are discussed.     

1985年澳大利亚高压与我国夏季降水的振荡关系

本文利用1985年6—8月气象资料和卫星云图资料,计算了南半球澳高地面气压与我国近35个台站24小时降水量的凝聚谱、位相谱,发现在准一周(约五天)周期处两者存在反位相振荡。又通过澳高地面气压与北半球有关环流系统的凝聚谱、位相谱分析,发现澳大利亚冷空气爆发与北半球夏季低纬和中纬行星尺度系统存在短周期准一周(约五天)左右遥相关。并且,东亚沿岸从南到北七个站850百帕经向风速,与澳高地面气压在周期五天左右处,有较高的凝聚平方值,风速增强过程有北传现象。      

An estimate of space-time correlations

Laboratory measurements of the autocorrelation and space-time correlations for probe separations alined with the mean flow are used to test a hypothesis of Pielke and Panofsky (1970) which relates these measures by means of an empirical decay parameter taken from coherence data. The direct laboratory measurements of the space-time correlations are in good agreement with the functions estimated using the method of Pielke and Panofsky (1970). However, the decay parameters implied for the laboratory measurements are much smaller than those reported for atmospheric turbulence.     

Turbulence in an almond orchard: Spatial variations in spectra and coherence

The spatial variability of turbulence in a fully-leafed almond orchard was studied. Two three-dimensional sonic anemometers were used to measure turbulence spectra and coherence at different vertical and lateral separations inside the canopy. Peak frequencies of the horizontal velocity components, normalized by local horizontal wind speed, are greater in the canopy crown than in the trunkspace. Peak-normalized frequencies for the vertical velocity power spectra are similar in the canopy crown and in the subcanopy trunkspace. Spectral slopes in the inertial subrange are more negative than those predicted with Kolmogorov's -2/3 theory. It is thought that the foliage elements act to short-circuit the eddy cascade. Lateral separation of the instruments in the subcanopy trunkspace has little effect on the shape of the velocity spectra. On the other hand, lateral and vertical velocity coherences between spatially separated sensors are low inside the canopy. These low coherences are due to the Eulerian length scales being of the same order of magnitude as the separation distances of the anemometers. Phase angles between velocity components are about zero for small separation distances. When the two instruments are separated by 9 m and one instrument is positioned in a row while the other is between two rows, vertical velocities are about 180 deg out of phase and the streamwise velocities are about 40 to 60 deg out of phase. These data support the contention that preferred differences occur between within- and between-row wind flow regimes.     

Vertical coherence and phase delay between wind components in strong winds below 20 m

Vertical coherence and phase delay between wind components in strong winds in the lowest 20 m over uniform terrain in New Zealand have been analysed. The vertical decay constants and slopes for the horizontal wind components could be described as linear functions of the ratio of vertical spacing to mean height (δz/z), with relatively little scatter. The decay constants for the lateral were smaller than for the longitudinal components, the slopes larger for the lateral components, as found previously. The coherence of vertical velocity is best described by exponential decay functions multiplied by a parameter which decreases linearly from 1 (for δz/z=0) to 0.5 (for δz/z=1). The decay constants increased linearly with δz/z, as in the case of the horizontal components. There were no significant phase differences for the vertical components. Lateral and vertical decay constants for the longitudinal wind component could be fitted to identical functions of δy/z and δz/z, respectively.     

云南盛夏大雨物理量因子的选取及效果检验

从物理量因子场与云南盛夏（７－８月）大雨作为预报量之间的相关系数计算入手，通过相关场分析来提取因子信息，经过不同组合试验，选出新的预报因子，检验表明，新的组合因子与预报量之间的相关性有明显提高。由此而建立的预报方程有较好的历史拟合率和较稳定的实际预报能力。     

云南盛夏大雨物理量因子的选取及效果检验

从物理量因子场与云南盛夏（7－8月）大雨作为预报量之间的相关系数计算入手，通过相关场分析来提取因子信息，经过不同组合试验，选出新的预报因子。检验表明，新的组合因子与预报量之间的相关性有明显提高。由此而建立的预报方程有较好的历史拟合率和较稳定的实际预报能力。     

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.     

Representativeness of wind measurements on a mesoscale grid with station separations of 312 m to 10 km

A field experiment was carried out in which wind speed and direction were measured over flat terrain at a height of 10 m using 13 identical instruments spaced logarithmically along two perpendicular 10 km lines. Station separations ranged from 312 m to 10 km. One-minute data from 11 sampling periods of duration 6 to 10 h were studied. p ]The statistics showed little dependence on whether the line of instruments was oriented along the wind or across the wind. The correlation coefficients between wind fluctuations at two stations separated by distance x were found to vary exponentially with x, with an integral distance scale on the order of 1 km. The integral time scale derived from the variation of the single station variances with averaging time was found to equal several minutes. At a station separation of 10 km, the correlation coefficients between the wind components at the two sites were calculated to be 0.24, 0.37, and 0.47 for averaging times of 1, 10, and 60 min, respectively. These values for the correlation coefficients correspond to root-mean-square differences in wind speed at the two stations of about 1.3, 1.0, and 0.7 m/s, respectively.Exponential formulas based on dimensional analysis are suggested for fitting these observations. It is found that the observations of spatial correlations are best fit if two independent integral distance scales are used — a boundary-layer distance scale of about 300 m that best applies to small station separations and a mesoscale distance scale of about 10 km that applies to larger station separations.     

A note on vertical coherence of streamwise turbulence inside and above a model plant canopy

Measurements of longitudinal turbulent velocity were made at pairs of levels inside and above a model plant canopy in the wind tunnel. It was found that above approximately the zero-plane displacement level, the coherence and phase results were similar in many respects to atmospheric data, but that deviations from this behaviour appeared deeper in the model canopy.     

A note on vertical coherence of wind measured in an urban boundary layer

The coherence, γ, between levels of the horizontal components of wind velocity are examined for data obtained on a 118-m tower at Victoria Dock, an urban site in Melbourne, Australia. The coherence is analysed to determine the influence of various parameters on its variation; it is found to be strongly dependent on f=n δz/U (n frequency, δz interlevel spacing and U the mean wind speed), and to a lesser degree on thermal stability and wind component. The empirical relation γ=exp(?af) is found to be reasonable and estimates of a are given. The data conform to observations reported at other sites.     

Turbulence characteristics along several towers

Observations from several towers are used to show how measurements of wind and temperature near the surface can be used to estimate the variances of the horizontal velocity and the dissipation rate up to the top of the towers, provided the roughness length is known. The roughness length usually varies with wind direction, and the traditional methods of estimating it tend to lead to over-estimates.Analysis of cross spectra between velocity components at different levels shows that Davenport's Geometrical Similarity is satisfied. Coherence falls off exponentially with the ratio of height interval to wavelength, and the decay parameter depends on Richardson number near the surface. Coherences at different sites show no significant differences in neutral air. The lateral velocity components have larger coherence and more time delay between levels than the horizontal components at all sites.Time delay and coherence are also discussed in other Cartesian directions, and it is suggested that these quantities, having relatively simple properties, can be used as building blocks for an empirical three-dimensional model of turbulence.Contribution No. 6951     

The validity of Taylor's hypothesis in the atmospheric surface layer

Taylor's hypothesis is tested over Lake Ontario and Nebraska. In both places large eddies travel more rapidly than the local wind. A simple model is proposed for this effect.A condition is suggested for Taylor's hypothesis to be satisfied based on consideration of coherence.     

On the instability of a planetary boundary layer with Rossby number similarity

In Part I (1975), a linear stability analysis with respect to the formation of longitudinal vortex rolls was given for aturbulent boundary layer of the atmosphere. However, that analysis investigated the effect of inflection point instability only; therefore it is applicable only to the case of neutral stratification. In Part II presented here, the analysis is extended to include the combined effect of inflection point instability and instability due to heating from below. In contrast with the result in Part I, the main result is that in considering both these effects, longitudinal vortex rolls can develop only if the boundary layer has an unstable stratification. Another important result is that the structure of developing vortex rolls and their growth-rates are universal in a boundary layer with Rossby-number similarity, i.e., they are independent of any external parameter. The same is true for the orientation of the vortex rolls: the angle between the axis of the rolls and the surface stress is independent of external parameters. The only quantity which is not universal is the phase speed, which indicates the speed with which the rolls move in a direction perpendicular to the vortex axis; this phase speed depends on the geostrophic wind and on the roughness-length. Paper presented at the XIIIth Biennual Fluid Dynamics Symposium 5–10 September, 1977, Olsztyn, Poland.