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Abstract.
This article considers analytical and numerical analysis of the stability of the classical and generalized Kolmogorov problem for the Navier-Stokes equations defined on a three-dimensional periodic stretched torus. In the work, a generalized form of the Orr-Sommerfeld equations is derived for the analysis of the linear stability of the main solution, and neutral curves are constructed. As a result of searching for disconnected solutions for the discrete problem, 22 disconnected solutions for the classical problem and 6 solutions for the generalized problem with linear stability of the basic solution are found. It is shown that the chaotic dynamics of the system for similar parameter values is determined by the found disconnected solutions.
Keywords:
linear stability analysis, Navier-Stokes equaitons, 3D Kolmogorov problem, disconnected solutions, pseudospectral method.
DOI: 10.14357/20790279240401
EDN: GRWYTN
PP. 3-13.
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