Experimental Evaluation of Kolmogorov’s -5/3 and 2/3 Power Laws in the Developing Turbulent Round Jet

Abstract

The current work investigates the validity of two cornerstone results of the Kolmogorov K41 theory of turbulence in terms of the typical power law representations viz. the -5/3 law for turbulence spectra and the 2/3 law for second order structure functions. The developing region of the jet has been chosen since it is an equilibrium flow once fully developed (but not necessarily in the development phase), it becomes fully developed over lengths that are practical on a laboratory scale and it is a high-intensity flow with accessibly resolvable scales in time and space. The developing region of the jet is thus the perfect testbed for these investigations, which can herein be accurately mapped using our in-house laser Doppler anemometry (LDA) system. The high turbulence intensity and high shear flow is challenging from a measurement technical perspective, which is perhaps why this flow is so underexplored. This software-driven LDA system was developed specifically to optimize measurement of high shear and high turbulence intensities accurately in challenging flows such as the turbulent round jet in air. The jet was investigated experimentally both in the developing (non-equilibrium) and in the developed regions (equilibrium). Velocity static moments at each point are first presented to show the time averaged flow behavior while the spatial energy spectra and second order structure functions are computed to evaluate the power laws postulated by Kolmogorov. Measurements from both the developed and from the developing parts of the jet are presented to show validity of the measurement technique and unveil the actual spectral shapes in the developing non-equilibrium region, respectively.