N-mode truncations of the three-dimensional Navier-Stokes equations with periodic boundary conditions are considered. We show that the solution of truncated model exhibits, under some assumptions concerning the external force, general properties of symmetry and invariance. A particular seven-mode truncation is then derived and investigated in detail by making use of numerical tools typical of dynamical systems. An intricate phenomenon is found with the significant presence of two- and three-dimensional tori. Among different transitions the one from quasiperiodicity to chaos in a three-torus appears of particular interest.
3-DIMENSIONAL NAVIER-STOKES EQUATIONS TRUNCATED ON A TORUS / Franceschini, Valter; Zanasi, Roberto. - In: NONLINEARITY. - ISSN 0951-7715. - 5:(1992), pp. 189-209.
3-DIMENSIONAL NAVIER-STOKES EQUATIONS TRUNCATED ON A TORUS
FRANCESCHINI, Valter;ZANASI, Roberto
1992
Abstract
N-mode truncations of the three-dimensional Navier-Stokes equations with periodic boundary conditions are considered. We show that the solution of truncated model exhibits, under some assumptions concerning the external force, general properties of symmetry and invariance. A particular seven-mode truncation is then derived and investigated in detail by making use of numerical tools typical of dynamical systems. An intricate phenomenon is found with the significant presence of two- and three-dimensional tori. Among different transitions the one from quasiperiodicity to chaos in a three-torus appears of particular interest.
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