Qualitative analysis of dynamics in Kolmogorov’s problem on a flow of a viscous incompressible fluid

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We numerically analyze the qualitative behavior of solutions in the two-dimensional problem on a periodic flow of a viscous incompressible fluid with an exciting force (the Kolmogorov problem). To construct an approximate solution, we use the Bubnov–Galerkin method based on spline approximations. We prove the convergence of the method to the solution of the problem in the weak sense. We compare the obtained results with the results of other authors as well as with the Galerkin method based on trigonometric polynomials and with a hybrid finite-volume finite-element method. We carry out a bifurcation analysis of the problem and indicate a scenario of passage from regular solutions to chaotic ones.