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Triple Decomposition of Velocity Gradient Tensor in Compressible Turbulence

Computer Electrical and Mathematical Science and Engineering Division (CEMSE), Extreme Computing Research Center (ECRC), King Abdullah University of Science and Technology (KAUST), Thuwal 23955, Saudi Arabia
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Academic Editor: Pavel Berloff
Fluids 2021, 6(3), 98; https://doi.org/10.3390/fluids6030098
Received: 8 February 2021 / Revised: 23 February 2021 / Accepted: 25 February 2021 / Published: 2 March 2021
(This article belongs to the Section Turbulence)
The decomposition of the local motion of a fluid into straining, shearing, and rigid-body rotation is examined in this work for a compressible isotropic turbulence by means of direct numerical simulations. The triple decomposition is closely associated with a basic reference frame (BRF), in which the extraction of the biasing effect of shear is maximized. In this study, a new computational and inexpensive procedure is proposed to identify the BRF for a three-dimensional flow field. In addition, the influence of compressibility effects on some statistical properties of the turbulent structures is addressed. The direct numerical simulations are carried out with a Reynolds number that is based on the Taylor micro-scale of Reλ=100 for various turbulent Mach numbers that range from Mat=0.12 to Mat=0.89. The DNS database is generated with an improved seventh-order accurate weighted essentially non-oscillatory scheme to discretize the non-linear advective terms, and an eighth-order accurate centered finite difference scheme is retained for the diffusive terms. One of the major findings of this analysis is that regions featuring strong rigid-body rotations or straining motions are highly spatially intermittent, while most of the flow regions exhibit moderately strong shearing motions in the absence of rigid-body rotations and straining motions. The majority of compressibility effects can be estimated if the scaling laws in the case of compressible turbulence are rescaled by only considering the solenoidal contributions. View Full-Text
Keywords: triple decomposition; compressible turbulence; velocity gradient tensor; homogeneous isotropic turbulence; basic reference frame triple decomposition; compressible turbulence; velocity gradient tensor; homogeneous isotropic turbulence; basic reference frame
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MDPI and ACS Style

Boukharfane, R.; Er-raiy, A.; Alzaben, L.; Parsani, M. Triple Decomposition of Velocity Gradient Tensor in Compressible Turbulence. Fluids 2021, 6, 98. https://doi.org/10.3390/fluids6030098

AMA Style

Boukharfane R, Er-raiy A, Alzaben L, Parsani M. Triple Decomposition of Velocity Gradient Tensor in Compressible Turbulence. Fluids. 2021; 6(3):98. https://doi.org/10.3390/fluids6030098

Chicago/Turabian Style

Boukharfane, Radouan; Er-raiy, Aimad; Alzaben, Linda; Parsani, Matteo. 2021. "Triple Decomposition of Velocity Gradient Tensor in Compressible Turbulence" Fluids 6, no. 3: 98. https://doi.org/10.3390/fluids6030098

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