Development of high vorticity in incompressible 3D Euler equations: Influence of initial conditions

Abstract

The incompressible three-dimensional ideal flows develop very thin pancake-like regions of increasing vorticity. These regions evolve with the scaling ω_max(t) ∝ l(t)^-2/3 between the vorticity maximum and pancake thickness, and provide the leading contribution to the energy spectrum, where the gradual formation of the Kolmogorov interval E_k ∝ k^−5/3 is observed for some initial flows. With the massive numerical simulations, we study the influence of initial conditions on the processes of pancake formation and the Kolmogorov energy spectrum development.