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

## TL;DR

This paper investigates how initial conditions affect the formation of thin vorticity pancakes and the development of the Kolmogorov energy spectrum in 3D incompressible Euler flows through extensive numerical simulations.

## Contribution

It provides new insights into the role of initial conditions in the evolution of vorticity structures and energy spectra in ideal fluid flows.

## Key findings

- Initial conditions significantly influence pancake formation.
- The Kolmogorov spectrum develops under certain initial flow configurations.
- Scaling laws of vorticity and pancake thickness are confirmed.

## Abstract

The incompressible three-dimensional ideal flows develop very thin pancake-like regions of increasing vorticity. These regions evolve with the scaling $\omega_{\max}(t)\propto\ell(t)^{-2/3}$ between the vorticity maximum and pancake thickness, and provide the leading contribution to the energy spectrum, where the gradual formation of the Kolmogorov interval $E_{k}\propto k^{-5/3}$ is observed for some initial flows [Agafontsev et. al, Phys. Fluids 27, 085102 (2015)]. With the massive numerical simulations, in the present paper we study the influence of initial conditions on the processes of pancake formation and the Kolmogorov energy spectrum development.