title: Dynamical pattern formation in two-dimensional fluids and Landau pole bifurcation.
abstract: A phenomenological theory is proposed to analyze the asymptotic dynamics of perturbed inviscid Kolmogorov shear flows in two dimensions. The phase diagram provided by the theory is in qualitative agreement with numerical observations, which include three phases depending on the aspect ratio of the domain and the size of the perturbation: a steady shear flow, a stationary dipole, and four traveling vortices. The theory is based on a precise study of the inviscid damping of the linearized equation and on an analysis of nonlinear effects. In particular, we show that the dominant Landau pole controlling the inviscid damping undergoes a bifurcation, which has important consequences on the asymptotic fate of the perturbation.
authors.affiliation: Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, 606-8501 Kyoto, Japan.
authors.forename: Shun
authors.initials: S
authors.lastname: Ogawa
authors.affiliation: Laboratoire J. A. Dieudonné, Université de Nice Sophia-Antipolis, UMR CNRS 7351, Parc Valrose, F-06108 Nice Cedex 02, France.
authors.forename: Julien
authors.initials: J
authors.lastname: Barré
authors.affiliation: Department of Mathematics, Kyoto University, 606-8502 Kyoto, Japan and CREST, JST, 606-8502 Kyoto, Japan.
authors.forename: Hidetoshi
authors.initials: H
authors.lastname: Morita
authors.affiliation: Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, 606-8501 Kyoto, Japan.
authors.forename: Yoshiyuki Y
authors.initials: YY
authors.lastname: Yamaguchi
mesh_terms: D003198:Computer Simulation; D016014:Linear Models; D008962:Models, Theoretical; D009038:Motion; D017711:Nonlinear Dynamics