Deviations from Taylor’s frozen hypothesis and scaling laws in inhomogeneous jet flows
Sukesh Roy, Joseph D. Miller, Gemunu H. Gunaratne
Abstract
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 $$\frac{2}{3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfrac> </mml:math> -law is satisfied. Spectral-energy density of the flow, although anisotropic, is consistent with the Kolmogorov–Obukhov $$\frac{5}{3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mrow> <mml:mn>5</mml:mn> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:mfrac> </mml:math> -law in the flow direction.