Effect of strong anisotropy on the dissipative and non-dissipative regimes of the second-order structure function

Abstract

We study the variations in second-order velocity structure functions (SFs) in the strongly anisotropic turbulent flow past a backward facing step. Time-resolved particle image velocimetry measurements were taken in a stationary turbulent flow past a backward facing step at Reynolds numbers 13,600, 9,000, and 5,500 based on the maximum velocity and step size. Large-scale anisotropic properties of the flow along with local small-scale turbulence characteristics were characterized in detail. Seven interrogation points distributed along points of different large-scale anisotropic characteristics systematically probed the influence of large-scale anisotropy on the second-order SFs. The velocity SFs at each interrogation point represent variance of velocity increments in the streamwise, transverse (wall normal), and the two principle directions of local deformation field. Logarithmic derivatives of the SFs captured the scale-dependent scaling characteristics at the small scales. Measurements revealed a strongly anisotropic large-scale flow with an intense turbulent free-shear layer downstream of the step. Comparison among second-order SFs reveals a mechanistic relationship between the mean flow deformation field, defined by the principle axis of deformation and the magnitude of eigenvalues, to the characteristic influence on SF scaling in the dissipative and non-dissipative scales. Specifically, we report that non-dissipative scaling between orthogonal directions does not differentially saturate if these directions are aligned with the principle axis of deformation. We also show that the relative root mean square of velocity components influences the level of exponent saturation in the dissipative scale regime.