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Truncations to 12, 14 and 18 modes of the Navier-Stokes equations on a two-dimensional torus. (English) Zbl 0572.76029
Three truncations of the Navier-Stokes equations on a two-dimensional torus are numerically investigated by making use of techniques based on bifurcation theory. The three truncations, to 12, 14 and 18 modes, respectively, are obtained by taking into account all the modes contained in balls of increasing radius. The behaviour of each model is described by three different stories which start from three distinct fixed points and develop parallely. Two stories are characterized by the presence of fixed points and periodic orbits, the third one involves also two- dimensional tori. The three truncations exhibit a surprisingly rich collection of bifurcations.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
76M99 Basic methods in fluid mechanics
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