On the higher order mixed structure functions in laboratory shear flow

Abstract

Structure functions to order 8 are determined from the longitudinal and transverse velocity fluctuations measured at a single point in high Reynolds number laboratory shear flow. We examine the relationship between mixed structure functions (which are explicitly zero in isotropic flow), and those of the longitudinal and transverse structure functions. Our results confirm recent findings using SO(3) symmetry decomposition [S. Kurien and K. R. Sreenivasan, Phys. Rev. E 62, 2206 (2000)] that show that the mixed structure functions have larger scaling exponents than those of the single component structure functions, i.e., the j=2 anisotropic sector structure function scaling exponent is greater than that of the j=0 isotropic sector. However, we also show that the ratio of the j=2 to j=0 sector scaling exponents systematically decreases with increasing order, suggesting that at higher orders there is persistence of anisotropy at the smallest scales. Difficulties in the analysis due to the difference in scaling exponents of the transverse and longitudinal structure functions are addressed.

Multiscale anisotropic fluctuations in sheared turbulence with multiple states

“…(i) By going to smaller and smaller scales, isotropy is recovered faster than previously thought. We argue that this is due to the existence of non vanishing anisotropic contributions from the j = 4 sector (see below) discarded or incorrectly measured in previous works [18,30,31]. (ii) We show that the anisotropic fluctuations of longitudinal and transverse velocity increments scale similarly.…”

“…On one hand, all phenomenological turbulence theories point toward a return-to-isotropy, at small enough scales [1][2][3]. On the other hand, measurements of anisotropic contributions as functions of scale separation has revealed persistent small-scale anisotropy in hydrodynamical turbulence [14][15][16][17][18], magneto-hydrodynamics [19,20], and passive scalar mixing [21,22]. The persistence of anisotropy as reported in Refs.…”

“…Similarly, simulations have until now managed to perform the SO(3) decomposition at low Reynolds numbers only [22], due to computational bottlenecks (see Supplemental Material at [25] for an estimate). Consequently, until now results concerning the multi-scale statistical properties of anisotropic fluctuations have been characterized by considerable scatter, thus calling into question their universal nature and in some instances even jeopardizing the fundamental postulate of small-scale isotropy [18]. The main features of this work are the following: First, we have achieved sufficiently high Reynolds numbers for a paradigmatic homogeneous shear configuration obtained from a random Kolmogorov Flow (RKF).…”

Direct numerical simulations of turbulence subjected to a straining and destraining cycle

“…Such an analysis can then be compared to results obtained in statistically steady homogeneous and nonhomogeneous anisotropic shear flows. 14,15,17,55,56 Our data can be used to extend such approaches to time dependent anisotropic flows ͑see, e.g., Ref. 57 in the context of decaying anisotropic turbulence͒.…”

“…Many basic topics in turbulence theory have been clarified in the idealized conditions of spatially homogeneous shear flows. For instance, fundamental issue of isotropy recovery at small scales has been successfully addressed both experimentally [14][15][16][17] and numerically. [18][19][20] Turbulence subjected to large-scale deformation has been considered in various papers since the seminal works of Batchelor 21 and Townsend.…”