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A phenomenological theory is proposed to analyze the asymptotic dynamics ofperturbed inviscid Kolmogorov shear flows in two dimensions. The phase diagramprovided by the theory is in qualitative agreement with numerical observations,which include three phases depending on the aspect ratio of the domain and thesize of the perturbation: a steady shear flow, a stationary dipole, and fourtraveling vortices. The theory is based on a precise study of the invisciddamping of the linearized equation and on an analysis of nonlinear effects. Inparticular, we show that the dominant Landau pole controlling the invisciddamping undergoes a bifurcation, which has important consequences on theasymptotic fate of the perturbation.

Dynamical pattern formations in two dimensional fluid and Landau pole bifurcation