Vortex dynamics in two-dimensional periodic shear layers

Abstract

In this work, the doubly periodic shear layers are employed to underpin the vortex dynamics associated with the perturbed free shear layers using the lattice Boltzmann method with the Bhatnagar–Gross–Krook collision model. The effect of (i) width between shear layers, (ii) modes of perturbation, (iii) the strength of perturbation, and (iv) thickness of a shear layer on roll-up formation, vortex interactions, pairings, and the generation of thin filaments is studied in detail with the evolution kinetic energy, enstrophy, and palinstrophy for Reynolds number, \(\text {Re}=30,000\). The formation of thin vorticity braids and vortex merging causes the production of vorticity gradients and a rise in the palinstrophy. No compelling interplay is observed with corotating or counter-rotating vortices for a minimum separation distance (\(S_1\)) between two opposite vorticity strips. The counter-force from each layer creates a jet whose properties differ from those of a single shear layer. However, the evolution of multiple pairs of shear layers produces smaller vortices of lower strength and enhances the growth of palinstrophy and decay of kinetic energy and enstrophy. The rise in the momentum thickness is observed for the interactive flows (\(S_2 \le S_1\)), while the non-interactive flow (\(S_2 > S_1\)) shows constant momentum thickness. The increased perturbation strength quickens the roll-up of shear layer and enhances the growth of palinstrophy. Thick shear layers evolves with dipole-like structures and slows down the decay of kinetic energy and enstrophy compared to thin shear layer flows. It generates family of thin vortex filaments and influences the rapid growth of vorticity gradients and positive Okubo–Weiss-Q-quantity.