Normal Collision of a Single-Dipole of Vortices with a Flat Boundary

Abstract

Vortex dynamics associated with the normal interaction of a self-propelled dipole with a no-slip boundary is studied for various Reynolds numbers. The simulations are performed using the lattice Boltzmann (LB) equation method with Bhatnagar–Gross–Krook (BGK) collision model. The formation and detachment of the boundary layers near the no-slip wall create a new dipole with the primary vortex which takes a circular trajectory before the next successive viscous rebounds. Small-scale structures appear due to the effect of shear instability and the roll-up of the boundary layer from the wall. The Reynolds numbers influence the dipole rebounds and are responsible for the collision intensity and vorticity production at the boundary. The global quantities kinetic energy, E(t), enstrophy, Ω(t) and palinstrophy, P(t) are measured as a function of dimensionless time (ζ) to quantify the effect of boundaries and Reynolds numbers on the vortex dynamics. The Ω(t) and P(t) evolve to a peak and E(t) decays faster at the time of the collision.