Numerical evidence of smooth self‐similar dynamics and possibility of subsequent collapse for three‐dimensional ideal flows (original) (raw)

Direct numerical simulations of the three-dimensional Euler equations at resolutions up to 2563 for general periodic flows and 8643 for the symmetric Taylor-Green vortex are presented. The spontaneous emergence of flat pancakelike structures that shrink exponentially in time is observed. A simple self-similar model that fits these observations is discussed. Focusing instabilities similar to those leading to streamwise vortices in the context of free shear layers [J. Fluid Mech. 143, 253 (1984)], are expected to subsequently concentrate the vorticity and produce isolated vortex filaments. A finite time singularity for the Euler equation is not excluded as the result of interactions among these filaments. 'CT. Bardos and U. Frisch, "R6gularitt d'un fluide parfait de donnkes