2014/01/27 by Shun Ogawa, Julien Barré, Hidetoshi Morita +1
Biochemistry, Genetics and Molecular Biology · Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #Bifurcation #Bifurcation diagram #Bifurcation theory #Classical mechanics #Fluid Dynamics and Turbulent Flows #Geomagnetism and Paleomagnetism Studies #Inviscid flow #Mathematical analysis #Mathematics #Mechanics #Nonlinear system #Oceanographic and Atmospheric Processes #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Quantum mechanics #Shear flow #Statistical physics #Turbulence #Vortex #physics.flu-dyn
paper · pdf · doi:10.1103/physreve.89.063007
published as Phys. Rev. E 89, 063007 (2014) · 9 pages, 7 figures
arxiv created 2014/01/27 · openalex publication_date 2014/06/12 · arxiv updated 2014/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.