On the Reynolds number dependence of velocity-gradient structure and dynamics

We seek to examine the changes in velocity-gradient structure (local streamline topology) and related dynamics as a function of Reynolds number ( $Re_{\unicode[STIX]{x1D706}}$ ). The analysis factorizes the velocity gradient ( $\unicode[STIX]{x1D608}_{ij}$ ) into the magnitude ( $A^{2}$ ) and normal...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 861; pp. 163 - 179
Main Authors Das, Rishita, Girimaji, Sharath S.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 25.02.2019
Subjects
Computer simulation
Conditioning
Dependence
Direct numerical simulation
Dynamic structural analysis
Dynamics
Fluid flow
Frameworks
JFM Papers
Mathematical models
Probability theory
Reynolds number
Statistical analysis
Statistical methods
Streamlines
Tensors
Topology
Velocity
Velocity gradient
Velocity gradients
turbulent flows
intermittency
isotropic turbulence
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Summary:We seek to examine the changes in velocity-gradient structure (local streamline topology) and related dynamics as a function of Reynolds number ( $Re_{\unicode[STIX]{x1D706}}$ ). The analysis factorizes the velocity gradient ( $\unicode[STIX]{x1D608}_{ij}$ ) into the magnitude ( $A^{2}$ ) and normalized-gradient tensor ( $\unicode[STIX]{x1D623}_{ij}\equiv \unicode[STIX]{x1D608}_{ij}/\sqrt{A^{2}}$ ). The focus is on bounded $\unicode[STIX]{x1D623}_{ij}$ as (i) it describes small-scale structure and local streamline topology, and (ii) its dynamics is shown to determine magnitude evolution. Using direct numerical simulation (DNS) data, the moments and probability distributions of $\unicode[STIX]{x1D623}_{ij}$ and its scalar invariants are shown to attain $Re_{\unicode[STIX]{x1D706}}$ independence. The critical values beyond which each feature attains $Re_{\unicode[STIX]{x1D706}}$ independence are established. We proceed to characterize the $Re_{\unicode[STIX]{x1D706}}$ dependence of $\unicode[STIX]{x1D623}_{ij}$ -conditioned statistics of key non-local pressure and viscous processes. Overall, the analysis provides further insight into velocity-gradient dynamics and offers an alternative framework for investigating intermittency, multifractal behaviour and for developing closure models.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2018.924