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Eighth International Symposium on Turbulence and Shear Flow Phenomena
August, 28-30, 2013, Poitiers, Futuroscope, France

DOI: 10.1615/TSFP8

FINITE REYNOLDS NUMBER EFFECTS ON THE PRESSURE SPECTRUM IN ISOTROPIC TURBULENCE FREE DECAY

pages 1-6
DOI: 10.1615/TSFP8.1890
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Краткое описание

The time evolution of the pressure spectrum Ep in freely decaying homogeneous isotropic turbulence (HIT) is investigated via Eddy-Damped Quasi-Normal Markovian (EDQNM) computations. It is well known that physical quantities associated to the energy spectrum evolve through power laws in HIT decay. For both low and high values of Reλ, the associated power law exponents of these laws are known to depend on the initial conditions, such as the slope of the energy spectrum at the large scales σ, with E(k→0,0) ∝ kσ. Batchelor (1951) and Lesieur et al. (1999) proposed theoretical frameworks to evaluate the power law exponents associated to the pressure decay statistics. These formulae, which relate pressure and energy decay, have been recovered by the use of several underlying hypothesis, such as Reλ→+∞ and the Joint Gaussian Assumption (JGA). Such hypothesis are not completely satisfied in experiments and numerical simulations, the departure from the theoretical background being caused by a number of effects such as saturation, intermittency and finite Reynolds numbers (FRN). As a consequence, theoretical predictions are rarely completely matched by experimental/ numerical results.
In the present work, FRN effects over the prediction of the pressure spectrum are quantified in order to recover information about pressure fluctuations in HIT decay. The first issue investigated is the presence of a plateau in the Kolmogorov (1941) compensated pressure spectrum. This plateau, which has been observed at very high Reλ (Reλ = O(104) in practise), disappears approaching moderate Reλ. More specifically, the appearance of a −5/3 region instead of the classical −7/3 Kolmogorov scaling in the pressure spectrum at very small scales is observed. This result justifies the lack of agreement of the Kolmogorov −7/3 scaling with several DNS reported in literature, which were performed at moderate Reλ.
The ratio between the pressure and velocity Taylor microscales λp is also analysed, the results being in very good agreement with the predictions by Batchelor (1951) and with the experiments available in open literature. Both large and small Reλ behaviours are analysed, and the relevance of the FRN effects is quantified.

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