Collective oscillation in two-dimensional fluid

TL;DR

This paper reports the discovery of large-scale collective oscillations in two-dimensional fluid flows governed by the Euler equations, arising from a Hopf bifurcation and explained by a self-consistent dynamic theory.

Contribution

It introduces the first observation of collective oscillations in 2D Euler flows and provides a theoretical framework explaining their emergence.

Findings

Large-scale oscillations observed in 2D Euler equations.

Oscillations linked to Hopf bifurcation near critical points.

A self-consistent theory explains the collective organization of vortices.

Abstract

Large-scale collective oscillation is discovered in the two-dimensional Euler equations. For initial conditions far from a base stationary flow, the system does not relax to the base stationary flow, but instead shows pairs of coherent vortices moving along the base stream line, which leads to large-scale oscillatory fields. The investigation of the vicinity of a bifurcation point suggests that this oscillation appears through Hopf bifurcation. Furthermore, a dynamic self-consistent theory explains that this oscillation results from the collective organization of a state of self-oscillation.