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Power-law exponent in the transition period of decay in grid turbulence

Published online by Cambridge University Press:  18 August 2015

L. Djenidi ,
Md. Kamruzzaman  and
R. A. Antonia
L. Djenidi*
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 NSW, Australia
Md. Kamruzzaman
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 NSW, Australia
R. A. Antonia
Affiliation:
Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 NSW, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Hot-wire measurements are carried out in grid-generated turbulence at moderate to low Taylor microscale Reynolds number $Re_{{\it\lambda}}$ to assess the appropriateness of the commonly used power-law decay for the mean turbulent kinetic energy (e.g. $k\sim x^{n}$, with $n\leqslant -1$). It is found that in the region outside the initial and final periods of decay, which we designate a transition region, a power law with a constant exponent $n$ cannot describe adequately the decay of turbulence from its initial to final stages. One is forced to use a family of power laws of the form $x^{n_{i}}$, where $n_{i}$ is a different constant over a portion $i$ of the decay time during the decay period. Accordingly, it is currently not possible to determine whether any grid-generated turbulence reported in the literature decays according to Saffman or Batchelor because the reported data fall in the transition period where $n$ differs from its initial and final values. It is suggested that a power law of the form $k\sim x^{n_{init}+m(x)}$, where $m(x)$ is a continuous function of $x$, could be used to describe the decay from the initial period to the final stage. The present results, which corroborate the numerical simulations of decaying homogeneous isotropic turbulence of Orlandi & Antonia (J. Turbul., vol. 5, 2004, doi:10.1088/1468-5248/5/1/009) and Meldi & Sagaut (J. Turbul., vol. 14, 2013, pp. 24–53), show that the values of $n$ reported in the literature, and which fall in the transition region, have been mistakenly assigned to the initial stage of decay.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 779 , 25 September 2015 , pp. 544 - 555
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Copyright
© 2015 Cambridge University Press 

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