Experimental study of the influence of anisotropy on the inertial scales   of turbulence
  We ask whether the scaling exponents or the Kolmogorov constants depend on the anisotropy of the velocity fluctuations in a turbulent flow with no shear. According to our experiment, the answer is no for the Eulerian second-order transverse velocity structure function. The experiment consisted of 32 loudspeaker-driven jets pointed toward the centre of a spherical chamber. We generated anisotropy by controlling the strengths of the jets. We found that the form of the anisotropy of the velocity fluctuations was the same as that in the strength of the jets. We then varied the anisotropy, as measured by the ratio of axial to radial root-mean-square (RMS) velocity fluctuations, between 0.6 and 2.3. The Reynolds number was approximately constant at around $R_\lambda$ = 481. In a central volume with a radius of 50 mm, the turbulence was approximately homogeneous, axisymmetric, and had no shear and no mean flow. We observed that the scaling exponent of the structure function was $0.70 \pm 0.03$, independent of the anisotropy and regardless of the direction in which we measured it. The Kolmogorov constant, $C_2$, was also independent of direction and anisotropy to within the experimental error of 4%. 
Kelken Chang, Gregory P. Bewley and Eberhard Bodenschatz
physics.flu-dyn