Compressibility effects on homogeneous isotropic turbulence using Schur decomposition of the velocity gradient tensor.

Abstract
The study of compressibility effects on the dynamics and the structure of turbulence is an important, but difficult, topic in turbulence modeling. Taking advantage of a recently proposed Schur decomposition approach (Keylock, C. J., The Schur decomposition of the velocity gradient tensor for turbulent flows, Journal of Fluid Mechanics, 2018) to decompose the velocity gradient tensor into its normal and non-normal parts, here we evaluate the influence of the compressibility on some statistical properties of the turbulent structures. We perform a set of direct numerical simulations of decaying compressible turbulence at six turbulent Mach numbers between Mt = 0.12 and Mt = 0.89 and a Reynolds number based on the Taylor micro-scale of Ret = 100. All the simulations have been carried out using an improved seventh-order accurate WENO scheme to discretize the non-linear advective terms and an eight-order accurate centered finite difference scheme is retained for the diffusive terms. In the double decomposition, the normal parts of the velocity gradient tensor (represented by the eigenvalues) are separated explicitly from non-normal components. The two-dimensional space defined by the second and third invariants of the velocity gradient tensor is subdivided into six regions and the contribution of each regional term to the Schur decomposition of the velocity gradient tensor is analyzed. Our preliminary findings show the difficulty of understanding the non-local effects without taking into account both the normal contribution (represented by the eigenvalues) and the non-normal component computed with of the Schur decomposition.

Citation
Boukharfane, R., Er-Raiy, A., & Parsani, M. (2021). Compressibility effects on homogeneous isotropic turbulence using Schur decomposition of the velocity gradient tensor. AIAA Scitech 2021 Forum. doi:10.2514/6.2021-1446

Acknowledgements
The research reported in this paper was funded by KAUST. We are thankful for the computer clusters at KAUST Supercomputing Laboratory (KSL) and the Supercomputing Laboratory and the Extreme Computing Research Center The authors thank Dr. Bilel Hadri at KSL for his technical assistance.

Publisher
American Institute of Aeronautics and Astronautics (AIAA)

Conference/Event Name
AIAA Science and Technology Forum and Exposition, AIAA SciTech Forum 2021

DOI
10.2514/6.2021-1446

Additional Links
https://arc.aiaa.org/doi/10.2514/6.2021-1446

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