Triple Decomposition of Velocity Gradient Tensor in Compressible Turbulence

Radouan Boukharfane,Linda Alzaben,Matteo Parsani,Aimad Er-Raiy

doi:10.3390/fluids6030098

Radouan Boukharfane, Linda Alzaben + Show 2 more

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https://doi.org/10.3390/fluids6030098

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Abstract

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.

Highlights

Turbulence in the context of fluid dynamics often refers to the chaotic nature of fluid motion in terms of velocity and pressure
For deterministic turbulent flows, some statistical laws apply in the same manner as for linear systems [2], whereas their statistics may widely differ; they usually are of Lévy-type and show long tail distributions that are produced by rare large-scale fluctuations and clustering phenomena of anomalous eddy diffusion
It provides more insights into the normal-strain and pure rotation on important small-scale features than those that were obtained by the more simple decomposition of A into symmetric, S, and anti-symmetric, W, parts. This decomposition suffers from the difficult task of identifying the basic reference frame (BRF) because it is based on the natural decomposition of fluid motion into straining, shearing, and rigid-body rotation

Summary

Introduction

Turbulence in the context of fluid dynamics often refers to the chaotic nature of fluid motion in terms of velocity and pressure This kind of definition suggests deterministic chaotic and turbulent characteristics [1], which must be distinguished from random behaviour. One of the first illustrations of this universal character dates back to 1941, when the Kolmogorov theory emerged The latter states that, regardless of a fluid’s properties, the turbulent flow exhibits a scale-invariant structure at the inertial region. Based on this finding, Kolmogorov was able to characterize this zone as a power law of the energy spectrum with an exponent that is equal to −5/3 [7], which for flows of Reynolds numbers smaller than infinity, is modified by an intermittency correction [8,9]

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