Deviations from Taylor’s frozen hypothesis and scaling laws in inhomogeneous jet flows

Abstract

Difficulties in studying turbulent flows stem, in part, from the lack of high-frequency, high-resolution measurements to interrogate small-scale structures and their rapid evolution. We present analysis of data from experiments employing a burst-mode laser system to capture both spatially resolved velocity fields and their dynamics using high-resolution particle image velocimetry measurements at 100 kHz. We show directly that velocity fluctuations in axisymmetric jet flows are inhomogeneous and anisotropic. The peak of the time-delayed cross correlation function decays exponentially in time and its velocity is smaller than the convection velocity; thus, Taylor’s frozen hypothesis fails to generalize for these inhomogeneous flows. Structure functions are isotropic only at small distances. They exhibit extended self-similarity, but no inertial range is found where the Kolmogorov 23-law is satisfied. Spectral-energy density of the flow, although anisotropic, is consistent with the Kolmogorov–Obukhov 53-law in the flow direction.