Nearly toroidal, periodic and quasi-periodic motions of fluid particles driven by the Gavrilov solutions of the Euler equations

TL;DR

This paper analyzes the fluid particle trajectories in Gavrilov's steady solutions of the 3D Euler equations, revealing nearly toroidal, periodic, and quasi-periodic motions through an ODE approach.

Contribution

It provides a detailed ODE analysis of Gavrilov's solutions, elucidating the complex particle dynamics in these steady fluid flows.

Findings

Fluid particles exhibit nearly toroidal trajectories.

Presence of periodic and quasi-periodic motions.

Enhanced understanding of Gavrilov's vector field dynamics.

Abstract

We consider the smooth, compactly supported solutions of the steady 3D Euler equations of incompressible fluids constructed by Gavrilov in 2019, and we study the corresponding fluid particle dynamics. This is an ode analysis, which contributes to the description of Gavrilov's vector field.