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Pressure statistics in self-similar freely decaying isotropic turbulence

Published online by Cambridge University Press:  07 February 2013

Marcello Meldi  and
Pierre Sagaut
Marcello Meldi*
Affiliation:
Institut Jean Le Rond d’Alembert, UMR 7190, 4 Place Jussieu, Case 162, Université Pierre et Marie Curie, Paris 6, F-75252 Paris CEDEX 5, France
Pierre Sagaut
Affiliation:
Institut Jean Le Rond d’Alembert, UMR 7190, 4 Place Jussieu, Case 162, Université Pierre et Marie Curie, Paris 6, F-75252 Paris CEDEX 5, France
*
†Email address for correspondence: marcellomeldi@gmail.com
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Abstract

The time evolution of pressure statistics in freely decaying homogeneous isotropic turbulence (HIT) is investigated via eddy-damped quasi-normal Markovian (EDQNM) computations. The present results show that the time decay rate of pressure-based statistical quantities, such as pressure variance and pressure gradient variance, are sensitive to the breakdown of permanence of large eddies. New formulae for the associated time-decay exponents are proposed, which extend previous relations proposed in Lesieur, Ossia & Metais (Phys. Fluids, vol. 11, 1999, p. 1535). Particular attention is paid to finite-Reynolds-number (FRN) effects on the pressure spectrum and pressure statistics. The results also suggest that $R{e}_{\lambda } = O(1{0}^{4} )$ must be considered to observe a one-decade inertial range in the pressure spectrum with Kolmogorov $- 7/ 3$ scaling. This threshold value is larger than almost all existing direct numerical simulation (DNS) and experimental data, justifying the discussion about other possible scaling laws. The $- 5/ 3$ slope reported in some DNS data is also recovered by the EDQNM model, but it is observed to be a low-Reynolds-number effect. Another important result is that FRN effects yield a departure from asymptotic theoretical behaviours which appear similar to some effects attributed to intermittency by most authors. This is exemplified by the ratio between pressure-based and velocity-based Taylor microscales. Therefore, high-Reynolds-number DNS or experiments such that $R{e}_{\lambda } = O(1{0}^{4} )$ would be required in order to remove FRN effects and to analyse pure intermittency effects.

JFM classification

Acoustics: Acoustics Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence theory
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 717 , 25 February 2013 , R2
Copyright
©2013 Cambridge University Press

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