Abstract
This article reviews some recent simulations of vortex sheet roll-up using the vortex blob method. In planar and axisymmetric flow, the roll-up is initially smooth but irregular small-scale features develop later in time due to the onset of chaos. A numerically generated Poincaré section shows that the vortex sheet flow resembles a chaotic Hamiltonian system with resonance bands and a heteroclinic tangle. The chaos is induced by a self-sustained oscillation in the vortex core rather than external forcing. In three-dimensional flow, an adaptive treecode algorithm is applied to reduce the CPU time from O(N 2) to O(N log N), where N is the number of particles representing the sheet. Results are presented showing the growth of azimuthal waves on a vortex ring and the merger of two vortex rings.
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Krasny, R., Lindsay, K., Nitsche, M. (2002). Simulation of vortex sheet roll-up: chaos, azimuthal waves, ring merger. In: Bajer, K., Moffatt, H.K. (eds) Tubes, Sheets and Singularities in Fluid Dynamics. Fluid Mechanics and Its Applications, vol 71. Springer, Dordrecht. https://doi.org/10.1007/0-306-48420-X_1
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DOI: https://doi.org/10.1007/0-306-48420-X_1
Publisher Name: Springer, Dordrecht
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