DOI: 10.1615/TSFP8
FINITE REYNOLDS NUMBER EFFECTS ON THE PRESSURE SPECTRUM IN ISOTROPIC TURBULENCE FREE DECAY
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/λ 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.