Abstract
The dynamics of three-dimensional ideal flows is investigated by direct numerical simulations of the Euler equations at resolutions up to 2563 for general periodic flows and 8643 for the symmetric Taylor-Green vortex. The spontaneous emergence of flat pancake-like structures that shrink exponentially in time is observed. A simple self- similar model that fits these observations is presented. Focusing instabilities similar to those leading to streamwise vortices in the context of free shear layers (15), are expected to subsequently concentrate the vorticity and produce isolated vortex filaments. A finite time singularity for the Euler equations is not excluded as the result of interactions among these filaments.
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Brachet, M.E., Meneguzzi, M., Vincent, A., Politano, H., Sulem, P.L. (1993). Can Three-Dimensional Ideal Flows Become Singular in a Finite Time?. In: Caflisch, R.E., Papanicolaou, G.C. (eds) Singularities in Fluids, Plasmas and Optics. NATO ASI Series, vol 404. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2022-7_3
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DOI: https://doi.org/10.1007/978-94-011-2022-7_3
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