Abstract
The local streamline topology classification method of Chong et al. (Phys. Fluids A: Fluid Dyn., vol. 2, no. 5, 1990, pp. 765–777) is adapted and extended to describe the geometry of infinitesimal vortex lines. Direct numerical simulation (DNS) data of forced isotropic turbulence reveals that the joint probability density function (p.d.f.) of the second ( $q_\omega$ ) and third ( $r_\omega$ ) normalized invariants of the vorticity gradient tensor asymptotes to a self-similar bell shape for $Re_\lambda > 200$ . The same p.d.f. shape is also seen at the late stages of breakdown of a Taylor–Green vortex suggesting the universality of the bell-shaped p.d.f. form in turbulent flows. Additionally, vortex reconnection from different initial configurations is examined. The local topology and geometry of the reconnection bridge is shown to be nearly identical in all cases considered in this work. Overall, topological characterization of the vorticity field provides a useful analytical basis for examining vorticity dynamics in turbulence and other fluid flows.
Highlights
The origins of the fields of vortex dynamics and topology are intricately intertwined (Moffatt 2008)
This indicates that the characteristic bell shape of the qω–rω distribution is unique in turbulent flow fields much like the characteristic teardrop-shape distribution observed for the velocity gradient invariants
Vortex line geometry classification, which is related to topology, is introduced using suitably normalized vorticity gradient invariants (Das & Girimaji 2019)
Summary
The origins of the fields of vortex dynamics and topology are intricately intertwined (Moffatt 2008). A recent study by Boschung et al (2014) presents a mathematical framework to investigate the local vortex line topology in terms of the curvature of a surface element normal to the local vorticity vector Such a description only provides information about the local divergence or convergence and rotation of the vortex lines. The current approach has the following advantages: (a) the framework can be used for identification of large-scale coherent vortex structures that occur in turbulent flows (Sharma, Das & Girimaji 2019), and (b) the vortex line shape characterization provides a higher order geometric description of the local streamline structure, using the Biot–Savart law. The initial configurations considered are (a) antiparallel (Melander & Hussain 1988) and (b) orthogonal (Boratav et al 1992) vortex tubes
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