Pattern formations in the 2D perfect fluids flows

小川 駿

10月25日(金) 13時30分

Patterns in effective 2D fluids are found in nature in various stages[1]. Statistical physics, Miller-Robert-Sommeria (MRS) theory in particular, has been used for explaining the formation of large vortices [2]. However MRS theory is sometimes difficult to use in practice, because it requires an infinite number of datas of invariants and vorticity levels. Then, I propose a dynamically theoretical method to analyze the asymptotic dynamics of perturbed 2D perfect fluids flows, in particular the perturbed Kolmogorov flow. The phase diagram parametrized with the aspect ratio of the doubly periodic domain and size of perturbations is constructed by the nonlinear Landau damping theory, and this diagram includes a zonal phase, dipole phase, and oscillating phase with the traveling vortices. This result is in qualitative agreement with the numerical observation by Morita [3].

This talk is based on the work with Julien Barr'e (Univ. Nice), Hidetoshi Morita (Kyoto univ.), and Yoshiyuki Y. Yamaguchi (Kyoto univ.).

[1] F. Bouchet and A. Venaille, Phys. Rep. 515, 227 (2012).
[2] J. Miller, Phys. Rev. Lett. 65, 2137 (1990);
R. Robert, J. Stat. Phys. 65, 531 (1991);
R. Robert and J. Sommeria, J. Fluids. Mech. 229, 291 (1991).
J. Miller, P. B. Weichman, and M. C. Cross, Phys. Rev. A 45, 2328 (1992).
[3] H. Morita, arXiv:1103.1140.