Direct Observation of Deviations from Taylor's Frozen Hypothesis and Scaling Laws in Canonical Jet Flows

Abstract The legendary 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. Our experiments, employing a burst-mode laser system, capture both spatially resolved velocity fields and their dynamics using high-resolution particle image velocimetry measurements at 100 kHz. We show directly that fluctuations of flow velocity in an axisymmetric jet flow are inhomogeneous and anisotropic. The velocity of the peak of the time-delayed cross correlation function C(r, r 0 ; τ ) is smaller than the convection velocity; thus Taylor’s frozen hypothesis [Taylor GI, Proc. R. Soc. London, Ser A 164, 476 (1938)] fails to generalize for inhomogeneous jet flows, consistent with prior studies. Its peak decays exponentially in time. Second, the structure functions are found to be isotropic at small distances, but not at large distances. Extended self-similarity is found to hold [Benzi R et al., Physics Review E 48, R29 (1993)], but no inertial range is found where the Kolmogorov 2 3 -law [Kolmogorov AN, Dokl. Akad. Naud. SSSR 30, 299 (1941)] holds. Spectral-energy density of the jet flow, although anisotropic, is consistent with the Kolmogorov-Obukhov 5 3 -law [Obukhov AM, Izvestiya Akad. Nauk. SSSR 32, 19 (1941)] in the flow direction.