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.