Compressible turbulent mixing: Effects of Schmidt number

Qionglin Ni
Phys. Rev. E 91, 053020 – Published 26 May 2015

Abstract

We investigated by numerical simulations the effects of Schmidt number on passive scalar transport in forced compressible turbulence. The range of Schmidt number (Sc) was 12525. In the inertial-convective range the scalar spectrum seemed to obey the k5/3 power law. For Sc1, there appeared a k1 power law in the viscous-convective range, while for Sc1, a k17/3 power law was identified in the inertial-diffusive range. The scaling constant computed by the mixed third-order structure function of the velocity-scalar increment showed that it grew over Sc, and the effect of compressibility made it smaller than the 43 value from incompressible turbulence. At small amplitudes, the probability distribution function (PDF) of scalar fluctuations collapsed to the Gaussian distribution whereas, at large amplitudes, it decayed more quickly than Gaussian. At large scales, the PDF of scalar increment behaved similarly to that of scalar fluctuation. In contrast, at small scales it resembled the PDF of scalar gradient. Furthermore, the scalar dissipation occurring at large magnitudes was found to grow with Sc. Due to low molecular diffusivity, in the Sc1 flow the scalar field rolled up and got mixed sufficiently. However, in the Sc1 flow the scalar field lost the small-scale structures by high molecular diffusivity and retained only the large-scale, cloudlike structures. The spectral analysis found that the spectral densities of scalar advection and dissipation in both Sc1 and Sc1 flows probably followed the k5/3 scaling. This indicated that in compressible turbulence the processes of advection and dissipation except that of scalar-dilatation coupling might deferring to the Kolmogorov picture. It then showed that at high wave numbers, the magnitudes of spectral coherency in both Sc1 and Sc1 flows decayed faster than the theoretical prediction of k2/3 for incompressible flows. Finally, the comparison with incompressible results showed that the scalar in compressible turbulence with Sc=1 lacked a conspicuous bump structure in its spectrum, but was more intermittent in the dissipative range.

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  • Received 11 February 2015

DOI:https://doi.org/10.1103/PhysRevE.91.053020

©2015 American Physical Society

Authors & Affiliations

Qionglin Ni*

  • State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, 100871, Beijing, People's Republic of China and Department of Physics, University of Rome Tor Vergata, Via della Ricerca Scientifica 1, 00133, Rome, Italy

  • *niql.pku@gmail.com

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Vol. 91, Iss. 5 — May 2015

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