Collective oscillation in two-dimensional fluid

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.