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Topological features and properties associated with development/decay of vortices in isotropic homogeneous turbulence
Phys. Rev. Fluids 2, 014701 – Published 6 January, 2017
DOI: https://doi.org/10.1103/PhysRevFluids.2.014701
Abstract
Topological features of vortices in terms of local flow geometry in an isotropic homogeneous turbulence and relationships between the topology and development of a vortex are investigated. Swirlity and sourcity represent the unidirectionality and intensities of the azimuthal and radial flows, respectively. Skewness reflects the symmetry quantity of the vortical flow. Together, the three quantities characterize the details of the invariant flow geometry. The analysis shows that flow symmetry is correlated with swirlity, and associated with its development or decay, especially for weak vortices. Stronger vortices exhibit lower correlations between the two and lack sufficient flow symmetry for inflow in all directions. This clarifies why highly intense vortices cannot attain effective vortex stretching. Vortex stretching is formulated in terms of the radial flow in the swirl plane. It shows that stretching is not entirely characterized by the eigenvalues of the rate-of-strain tensor, and depends on the eigenvalues of the radial flow classified by sourcity. Sourcity shows that numerous vortices, which have been classified as inflow (convergent) vortices using the complex eigenvalues of the velocity gradient tensor, have a mixture of inflow and outflow. These vortices break the orthogonality of the vortical axis to the swirl plane during vortex stretching. Stretching in vortices with complete inflow increases vorticity normal to the swirl plane effectively and improves axis orthogonality. Sourcity classifies these characteristics, and flow symmetry and sourcity are important quantities for effective stretching. The present topological analysis provides important details of vortical flow features in turbulent flows or realistic vortex models, and sourcity extracts the specific vortical region supported by the flow geometry itself.
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