Experimental study of the influence of anisotropy on the inertial scales of turbulence

Abstract

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 (r.m.s.) velocity fluctuations, between 0.6 and 2.3. The Reynolds number was approximately constant at around R λ = 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 ± 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 %.

On integral length scales in anisotropic turbulence

“…As reported by Chang, Bewley, and Bodenschatz, 12 scaling exponents for the second-order structure functions were isotropic, and Eq. (6) was fulfilled in the inertial range, as required by assumptions 3 and 4.…”

“…11 Our apparatus generated statistically stationary turbulence with tunable anisotropy, and is described in detail by Chang, Bewley, and Bodenschatz. 12 We give a brief summary here. Thirty-two loudspeaker-driven air jets pointed toward the center of a spherical chamber.…”

Turbulent flow of a fluid with anisotropic viscosity

“…At zero magnetic field, the profiles appear similar with only a small anisotropy. While the flow should be isotropic, this appears not to be unusual (Chang et al 2012). The anisotropy arises most probably from small asymmetries in the flow cell.…”

“…Anisotropy is generated using a paramagnetic colloid whose viscosity depends both on the direction and magnitude of an external † Email address for correspondence: roesgen@ifd.mavt.ethz.ch magnetic field. Our approach is thus fundamentally different from other experiments studying anisotropic turbulence where anisotropy is produced for example by rotation (Lamriben, Cortet & Moisy 2011), mean velocity gradients (Shen & Warhaft 2000) or by modulation of many mixers inside a flow chamber (Chang, Bewley & Bodenschatz 2012). Uniform magnetic field forcing has so far been used primarily in studies on the global evolution of laminar and transitional flows (Altmeyer et al 2010;Reindl & Odenbach 2011).…”

Turbulence in the interstellar medium

“…This theory of turbulence has been quite successful in reproducing most of the experimental data, and there is a flourishing literature with hundreds of works available, e.g. Armstrong et al, 1995;Leamon et al, 1998;Bale et al, 2005;Koga et al, 2007;Bourras et al, 2009;Chian and Miranda, 2009;Chepurnov and Lazarian, 2010;Sahraoui et al, 2010;Chian and Muñoz, 2011;Chang et al, 2012;Hurricane et al, 2012;Miranda et al, 2013, just to mention a few. Naturally, many authors criticised the fact that C(p) is a constant in Kolmogorov's initial theory, given the breakdown of self-similarity at small scales and the possible non-universality of turbulence (given its "memory" related to the energy injection).…”