Journal of Applied Nonlinear Dynamics 6(3) (2017) 345--353 | DOI:10.5890/JAND.2017.09.003

Nikolai M. Evstigneev; Nikolai A. Magnitskii

Institute for Systems Analysis, Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, Russia

Abstract

A three dimensional Kolmogorov problem with extended forcing term for Navier-Stokes equations is considered. The Galerkin-Fourier method is applied and the symmetry preserving subset of solutions is considered. The bifurcation patterns are revealed through the numerical analysis of eigenvalues of the linearized perturbed system from the analytical main stationary solution and through the analysis of phase space trajectories that the system generates. It was found that the initial stage of laminar-turbulent transition undergoes pitchfork bifurcation, through which the system can either go through the series of cycle cascades or through continuous tori bifurcations in accordance with the FShM scenario.

Acknowledgments

The work is supported by the Russian Found of Fundamental Research (grant RFFR 17-07-00116) and by the grant ONIT RAS 4.

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