On the Reynolds number dependence of velocity-gradient structure and dynamics Academic Article uri icon

abstract

  • 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.

published proceedings

  • JOURNAL OF FLUID MECHANICS

altmetric score

  • 0.25

author list (cited authors)

  • Das, R., & Girimaji, S. S.

citation count

  • 9

complete list of authors

  • Das, Rishita||Girimaji, Sharath S

publication date

  • February 2019