Extraction of Anisotropic Contributions in Turbulent Flows

Abstract

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-...

Spectrum of anisotropic exponents in hydrodynamic systems with pressure

“…Experiments and simulations on Navier-Stokes (NS) turbulence also indicate that anisotropic sectors possess larger scaling exponents than the isotropic sector [2][3][4]. However, to date, the exponents for ℓ > 2 were not determined with sufficient accuracy.…”

“…Instead, components of the structure functions that belong to different irreducible representations (sectors) of the SO(3) group possess different scaling exponents. Each of these sectors is characterized by the angular momentum indices ℓ and m. By projecting the structure function onto the different sectors, we could measure [2][3][4] the universal scaling exponents in each sector separately.…”

Turbulence with pressure: Anomalous scaling of a passive vector field

“…in Refs. [57][58][59][60][61][62] for description of the NS turbulence. This becomes especially clear if the left-hand side of Eq.…”

The reflection-antisymmetric counterpart of the Kármán–Howarth dynamical equation

“…The decomposition of the structure function into rotationally invariant, irreducible subgroups of the SO(3) symmetry group S j=0 αβ (r)+S j=1 αβ (r)+... allowed the separation of the isotropic (indexed by j = 0) from the anisotropic (indexed by j > 0) contributions to the structure function. This procedure has allowed better quantification of the rate of decay of anisotropy of the small scales in turbulence [6,7,8]. These analyses considered homogeneous, isotropic and reflection symmetric flows.…”