Experimental investigation of scale-to-scale anisotropy and energy transfer in homogeneous axisymmetric turbulence

We experimentally investigate scale-to-scale anisotropy and energy transfer in homogeneous axisymmetric turbulence with negligible mean shear, strain, and mean flow. The turbulence was generated by two facing arrays of randomly actuated jets, and the Reynolds number Reλ was adjusted from 250 to 606. The velocity is measured by planar particle image velocimetry. Large-scale anisotropy was introduced by the geometric arrangement of the jet arrays, which drive the flow in the apparatus. We define the axial and the radial direction in our system as the directions parallel and perpendicular to the jets, respectively. We first examine the anisotropy of the turbulence scale-by-scale. At large scales, the measured integral length in the axial direction is greater than the one in the radial direction, indicating strong anisotropy introduced by energy injection. At inertial scales, the two-point Eulerian statistics is evaluated for both directions: the measured scaling exponents of the velocity structure functions are found to be consistent and in good agreement with the predictions by the intermittency model. At dissipative scales, the generalized flatness factors of the longitudinal velocity increments and the invariants of the velocity gradient tensor exhibit a high degree of isotropy. The trend toward isotropy at small scales is enhanced with increasing Reynolds number. We then investigate the behavior of the energy transfer by using the Kármán–Howarth–Monin–Hill equation to decouple the inter-scale and intra-scale energy flux. In scale space, the anisotropic energy distribution manifests itself as the discrepancy in the third-order structure functions at large scales, which further complicates the dynamics of energy transfer. In particular, energy is injected into the system axially, redistributed radially at large scales, and concurrently transferred to smaller scales via a forward energy cascade.