Passive scalar decay laws in isotropic turbulence: Prandtl number effects

Abstract

International audienceThe passive scalar dynamics in a freely decaying turbulent flow is studied. The classical framework of homogeneous isotropic turbulence without forcing is considered. Both low and high Reynolds number regimes are investigated for very small and very large Prandtl numbers. The long time behaviours of integrated quantities such as the scalar variance or the scalar dissipation rate are analyzed by considering that the decay follows power laws. This study addresses three major topics. Firstly, the Comte-Bellot and Corrsin (CBC) dimensional analysis for the temporal decay exponents is extended to the case of a passive scalar when the permanence of large eddies is broken. Secondly, using numerical simulations based on eddy-damped quasi-normal markovian (EDQNM) model, the time evolution of integrated quantities is accurately determined for a wide range of Reynolds and Prandtl numbers. These simulations show that, whatever the Reynolds and the Prandtl numbers are, the decay follows an algebraic law with an exponent very close to the value predicted by the CBC theory. Finally, the initial position of the scalar integral scale L T has no influence on the asymptotic values of the decay exponents, and an analytical law predicting the relative positions of the kinetic and scalar spectra peaks is derived

Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence

“…The results presented here are an extension of an analysis previously applied to the passive scalar in HIT (Briard et al 2015). The theoretical decay exponents of kinetic and scalar integrated quantities are recalled in Table 3.…”

“…These parameters p and p T reflect the strong backscatter of energy for the velocity and scalar fields respectively, that can occur in the infrared range notably for the Batchelor case. In particular, p T slightly depends on the Prandtl number and much more on the kinetic infrared slope σ (Briard et al 2015). In figure 5, large Reynolds numbers scalar decay exponents are recovered for Saffman and Batchelor shear-released turbulence.…”

“…In isotropic turbulence, the decay exponents of scalar integrated quantities such as the scalar variance K T and the scalar dissipation rate ǫ T are well-known since Comte-Bellot & Corrsin (1966) and are recalled in Table 3 following the work of Briard et al (2015). For the scalar variance…”

“…Then, we assume that the main contribution to the decay mechanism comes from the inertial range and consequently, that only the k −7/3 inertial range should be taken into account to determine the decay exponents of F . Secondly, in the case of Batchelor turbulence, when the permanence of large eddies hypothesis is broken, backscatter parameters p and p T are introduced for the velocity and scalar fields respectively in HIT (Briard et al 2015). Since F is the spectral counterpart of the velocity-scalar cross correlation, its backscatter parameter p F should contain both effects.…”

Decay and growth laws in homogeneous shear turbulence

“…This has been recovered recently for very large Reynolds numbers with a classical eddy-damped quasinormal Markovian (EDQNM) closure. [11][12][13] To quantify the impact of anisotropy on the decay regime, comparisons are usually made with homogeneous isotropic turbulence (HIT). Moreover, the case of axisymmetric contraction (or expansion), which is representative of grid turbulence, has already received some attention.…”