BEHAVIOR OF A 3-TORUS IN TRUNCATED NAVIER-STOKES EQUATIONS

The presence of a three-torus in a seven-mode truncation of the three- dimensional Navier-Stokes equations is investigated numerically by mea ns of cross-section and power spectra. Furthermore, by taking advantag e of particular features of the model, rotation vectors, circle maps a nd torus maps can be computed with high accuracy and used to study the dynamics. In particular, some interesting phenomena of partial phase- locking are described in deep detail. The three-torus, which arises vi a a Hopf bifurcation and persists in a wide parameter range, is found to break and originate a strange attractor. The onset of chaos and the associated bifurcation point can be defined quite precisely.