Vorticity dynamics - III

In this lecture, we explored the interactions between pairs of co-rotating and counter-rotating point vortices or vortex lines, analyzing how their mutual induction influences their trajectories. We introduced the concept that a vortex ring, due to its self-induced velocity field, undergoes axial translation. Furthermore, we discussed that a system of four or more interacting point vortices can give rise to complex, chaotic motion in two-dimensional flows, offering a simplified model for studying aspects of two-dimensional turbulence. In the latter part of the lecture, we examined the solid-body rotation of a fluid contained within a rotating cylindrical vessel. The pressure distribution within the fluid was derived, revealing that at any fixed vertical position, the pressure attains a minimum at the center of the vortex.