2 research outputs found
Dynamics of circular arrangements of vorticity in two dimensions
The merger of two like-signed vortices is a well-studied problem, but in a
turbulent flow, we may often have more than two like-signed vortices
interacting. We study the merger of three or more identical co-rotating
vortices initially arranged on the vertices of a regular polygon. At low to
moderate Reynolds numbers, we find an additional stage in the merger process,
absent in the merger of two vortices, where an annular vortical structure is
formed and is long-lived. Vortex merger is slowed down significantly due to
this. Such annular vortices are known at far higher Reynolds numbers in studies
of tropical cyclones, which have been noticed to a break down into individual
vortices. In the pre-annular stage, vortical structures in a viscous flow are
found here to tilt and realign in a manner similar to the inviscid case, but
the pronounced filaments visible in the latter are practically absent in the
former. Interestingly at higher Reynolds numbers, the merger of an odd number
of vortices is found to proceed very differently from that of an even number.
The former process is rapid and chaotic whereas the latter proceeds more slowly
via pairing events. The annular vortex takes the form of a generalised
Lamb-Oseen vortex (GLO), and diffuses inwards until it forms a standard
Lamb-Oseen vortex. For lower Reynolds number, the numerical (fully nonlinear)
evolution of the GLO vortex follows exactly the analytical evolution until
merger. At higher Reynolds numbers, the annulus goes through instabilities
whose nonlinear stages show a pronounced difference between even and odd mode
disturbances. It is hoped that the present findings, that multiple vortex
merger is qualitatively different from the merger of two vortices, will
motivate studies on how multiple vortex interactions affect the inverse cascade
in two-dimensional turbulence.Comment: Abstract truncated. Paper to appear in Physical Review