Abstract
An octahedral, vortical (divergence-free) flow is defined, and reasons are given for why it is a candidate for self-similar, point-collapse and blowup under evolution of the Euler equations. Results from a vortex filament model of such flows are then reviewed and the data subsequently analyzed. The Gauss map, a mapping of the vorticity tangent field, is examined. A Leray-Beltrami flow, defined as a force-free flow in the Leray collapse frame, is shown to develop in the inner region. Finally, the vorticity is found to scale as the inverse square of the distance from the origin, the center of the point collapse. A discussion follows on the ramification of these findings to possible blowup in the Navier-Stokes equations.
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Pelz, R.B. (2001). Analysis of a Candidate Flow For Hydrodynamic Blowup. In: Ricca, R.L. (eds) An Introduction to the Geometry and Topology of Fluid Flows. NATO Science Series, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0446-6_17
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DOI: https://doi.org/10.1007/978-94-010-0446-6_17
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