Dynamical pattern formation in two-dimensional fluids and Landau pole bifurcation

Shun Ogawa (1) , Julien Barré (2) , Hidetoshi Morita (3) , Yoshiyuki Y. Yamaguchi (1)

1 Department of Applied Mathematics and Physics [Kyoto]
2 JAD - Laboratoire Jean Alexandre Dieudonné
3 Department of Mathematics [Kyoto]

A phenomenological theory is proposed to analyze the asymptotic dynamics of perturbed inviscid Kol-mogorov shear flows in two dimensions. The phase diagram provided by the theory is in qualitative agree-ment 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.

Mots clés: 4754-r; 4715ki; 0545-a

Domaines: Physique [physics]

Shun Ogawa, Julien Barré, Hidetoshi Morita, Yoshiyuki Y. Yamaguchi. Dynamical pattern formation in two-dimensional fluids and Landau pole bifurcation. Physical Review Online Archive (PROLA), 2014, 89, pp.9. ⟨10.1103/PhysRevE.89.063007⟩. ⟨hal-01086377⟩