We analyze turbulent velocity signals in the atmospheric surface layer, obtained by pairs of probes separated by inertial-range distances parallel to the ground and (nominally) orthogonal to the mean wind. The Taylor microscale Reynolds number ranges up to 20 000. Choosing a suitable coordinate system with respect to the mean wind, we derive theoretical forms for second order structure functions and fit them to experimental data. The effect of flow anisotropy is small for the longitudinal component but significant for the transverse component. The data provide an estimate for a universal exponent from among a hierarchy that governs the decay of flow anisotropy with the scale size.[S0031-9007(98)07959-9] PACS numbers: 47.27. Gs, 05.40. + j, 47.27.Jv, 94.10.Jd Experimental studies of turbulent flows at very high Reynolds numbers are usually limited in the sense that one measures the velocity field at a single spatial point as a function of time [1], and uses Taylor's hypothesis to identify velocity increments at different times with those across spatial length scales, R. The standard outputs of such measurements are the longitudinal twopoint differences of the Eulerian velocity field and their moments, termed structure functions:where ͗?͘ denotes averaging over time. In homogeneous and isotropic turbulence, these structure functions are observed to vary as a power law in R, S n ͑R͒ ϳ R z n , with apparently universal scaling exponents z n [2]. [4] begins to offer information about the tensorial nature of structure functions. Ideally, one would like to measure the tensorial nth order structure functions defined as S a 1 ···a n n ͑R͒ ϵ ͓͗u a 1 ͑r 1 R͒ 2 u a 1 ͑r͔͒ 3 ͓u a 2 ͑r 1 R͒ 2 u a 2 ͑r͔͒ · · · ͓u a n ͑r 1 R͒ 2 u a n ͑r͔͒͘ , Recent progress in measurements [3] and in simulationswhere the superscript a i indicates the velocity component in the direction i. Such information should be useful in studying the anisotropic effects induced by all practical means of forcing.In analyzing experimental data the model of "homogeneous and isotropic small scale" is universally adopted, but it is important to examine the relevance of this model for realistic flows. One of the points of this Letter is that keeping the tensorial information helps significantly in disentangling different scaling contributions to structure functions [5]. Especially when anisotropy might lead to different scaling exponents for different tensorial components, a careful study of the various contributions is needed. We will show below that atmospheric measurements contain important anisotropic contributions to one type of transverse structure functions.We analyze measurements in atmospheric turbulence at heights of 6 and 35 m above the ground (data sets I and II). Set I was acquired over a flat desert with a long fetch, and the Taylor microscale Reynolds number was about 10 000. Set II was acquired over a rough terrain with illdefined fetch, and the microscale Reynolds number was 20 000 [6]. The data were acquired simultaneously from two single hot-...

Thrbulence velocity measurements have been made in the surface layer of the atmosphere at Taylor microscale Reynolds numbers between 10,000 and 20,000. Even at these high Reynolds numbers, the structure functions do not scale unambiguously. It is shown that the scaling improves significantly by implementing a plausible correction due to the mean shear. For second and fourth order structure functions, the exponents for the corrected data are close to those determined by extended self-similarity (ESS). ESS improves scaling enormously for all orders, and is used to obtain exponents for moment orders between -0.08 and 10. Anomaly prevails even for very low orders. A major qualitative conclusion is that it is difficult to discuss the scaling effectively without first understanding quantitatively the effects of finite shear and finite Reynolds numbers. §1.

Transverse structure functions are obtained at high Reynolds numbers in atmospheric turbulence ͑Taylor microscale Reynolds numbers between 10 000 and 15 000͒. These measurements confirm that their scaling exponents are different from those for longitudinal structure functions. Implications of this conclusion are discussed briefly. ͓S1063-651X͑97͒50511-3͔ PACS number͑s͒: 47.27. Ak, 47.27.Jv Anomalous scaling in turbulence has been studied traditionally in terms of the so-called longitudinal structure functions ͑LSF's͒, which are moments of velocity increments ⌬u r ϵu(xϩr)Ϫu(x), where u is the velocity component in a certain direction x and the separation distance r is measured also in the same direction. For most flows, experimental convenience necessitates that the direction x be that of the mean flow. Several attempts ͓1-10͔ have been made recently to obtain the so-called transverse structure functions ͑TSF's͒, which are moments of velocity increments for which the separation distance is transverse to the direction of the velocity component considered. A few of these measurements ͑e.g., Refs. ͓1,2,6͔͒ suggest ͑or imply͒ that the scaling exponents for TSF are equal, to within experimental uncertainties, to those for LSF. If the two sets of exponents are indeed equal, the hierarchy of models built up on the basis of LSF ͑see, e.g., Ref. ͓11͔͒ remains essentially intact. On the other hand, there exist measurements ͓3-5,8-10͔ purporting to show that the transverse exponents of order greater than 2 are measurably smaller than the longitudinal exponents. If true, this observation calls for additional complexity in smallscale phenomenology-and might even suggest the absence of strict scaling in the problem.To make a convincing case that high-order TSF exponents are smaller than those of LSF, it must first be shown that the inertial-range scales are isotropic. A minimum condition for local isotropy to exist is that the second-order exponents in the inertial range should be equal for LSF and TSF. It is known ͑e.g., Ref. ͓12͔, Fig. 5͒ that this requires, in shear flows, a Taylor microscale Reynolds number of the order of 1000 and higher. All the results cited above have been obtained at modest Reynolds numbers. Some of them have been made in shear flows. One might therefore wonder if the observed differences between the two sets of exponents are due perhaps to the lack of isotropy in the inertial range. Further, the scaling range at moderate Reynolds number is modest at best.In this context, we have made a series of measurements in atmospheric turbulence at Taylor microscale Reynolds numbers ranging between 10 000 and 15 000. These Reynolds numbers are comparable to the highest ever used for studies of small-scale turbulence ͑e.g., ͓13,14͔͒. Here, we examine the velocity data solely to address the following issue: Are there genuine differences between the longitudinal and transverse exponents? As already remarked, this question is important for the theory of small-scale turbulence.The velocity data were acquired by mea...

It is now believed that the scaling exponents of moments of velocity increments are anomalous, or that the departures from Kolmogorov's (1941) self-similar scaling increase nonlinearly with the increasing order of the moment. This appears to be true whether one considers velocity increments themselves or their absolute values. However, moments of order lower than 2 of the absolute values of velocity increments have not been investigated thoroughly for anomaly. Here, we discuss the importance of the scaling of non-integer moments of order between +2 and −1, and obtain them from direct numerical simulations at moderate Reynolds numbers (Taylor microscale Reynolds numbers R λ 450) and experimental data at high Reynolds numbers (R λ ≈ 10,000). The relative difference between the measured exponents and Kolmogorov's prediction increases as the moment order decreases towards −1, thus showing that the anomaly that is manifest in high-order moments is present in low-order moments as well. This conclusion provides a motivation for seeking a theory of anomalous scaling as the order of the moment vanishes. Such a theory does not have to consider rare events-which may be affected by non-universal features such as shear-and so may be regarded as advantageous to consider and develop.

We study some elementary statistics of wind direction fluctuations in the atmosphere for a wide range of time scales ͑10 Ϫ4 sec to 1 h͒, and in both vertical and horizontal planes. In the plane parallel to the ground surface, the direction time series consists of two parts: a constant drift due to large weather systems moving with the mean wind speed, and fluctuations about this drift. The statistics of the direction fluctuations show a rough similarity to Brownian motion but depend, in detail, on the wind speed. This dependence manifests itself quite clearly in the statistics of wind-direction increments over various intervals of time. These increments are intermittent during periods of low wind speeds but Gaussian-like during periods of high wind speeds.