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Symmetric vortex merger in two dimensions: Causes and conditions. (English) Zbl 0653.76020
Two like-signed vorticity regions can pair or merge into one vortex. This phenomenon occurs if the original two vortices are sufficiently close together, that is, if the distance between the vorticity centroids is smaller than a certain critical merger distance, which depends on the initial shape of the vortex distributions. Our conclusions are based on an analytical/numerical study, which presents the first quantitative description of the cause and mechanism behind the restricted process of symmetric vortex merger.
We use two complementary models to investigate the merger of identical vorticity regions. The first, based on a recently introduced low-order physical-space moment model of the two-dimensional Euler equations, is a Hamiltonian system of ordinary differential equations for the evolution of the centroid position, aspect ratio and orientation of each region. By imposing symmetry this system is made integrable and we obtain a necessary and sufficient condition for mergestems accounts for the amplification of fluctuations. The experimental transients for the onset of the convective pattern are shown to be theoretically reproducible.

MSC:
76B47 Vortex flows for incompressible inviscid fluids
76M99 Basic methods in fluid mechanics
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