Asymptotic solution for high vorticity regions in incompressible 3D Euler equations

TL;DR

This paper presents an exact asymptotic solution for high vorticity pancake regions in 3D Euler equations, combining shear and asymmetric strain, validated by detailed numerical simulations.

Contribution

It introduces a novel exact solution describing the evolution of high vorticity regions in 3D Euler flows, incorporating asymmetry and arbitrary vorticity profiles.

Findings

The solution accurately models pancake-like vorticity structures.

Numerical simulations confirm the solution's validity.

The approach enhances understanding of vorticity amplification in Euler flows.

Abstract

Incompressible 3D Euler equations develop high vorticity in very thin pancake-like regions from generic large-scale initial conditions. In this work we propose an exact solution of the Euler equations for the asymptotic pancake evolution. This solution combines a shear flow aligned with an asymmetric straining flow, and is characterized by a single asymmetry parameter and an arbitrary transversal vorticity profile. The analysis is based on detailed comparison with numerical simulations performed using a pseudo-spectral method in anisotropic grids of up to 972 x 2048 x 4096.