  We formulate and study a low-order nonlinear coupled ocean-atmosphere model
with an emphasis on the impact of radiative and heat fluxes and of the
frictional coupling between the two components. This model version extends a
previous 24-variable version by adding a dynamical equation for the passive
advection of temperature in the ocean, together with an energy balance model.
  The bifurcation analysis and the numerical integration of the model reveal
the presence of low-frequency variability (LFV) concentrated on and near a
long-periodic, attracting orbit. This orbit combines atmospheric and oceanic
modes, and it arises for large values of the meridional gradient of radiative
input and of frictional coupling. Chaotic behavior develops around this orbit
as it loses its stability; this behavior is still dominated by the LFV on
decadal and multi-decadal time scales that is typical of oceanic processes.
Atmospheric diagnostics also reveals the presence of predominant low- and
high-pressure zones, as well as of a subtropical jet; these features recall
realistic climatological properties of the oceanic atmosphere.
  Finally, a predictability analysis is performed. Once the decadal-scale
periodic orbits develop, the coupled system's short-term instabilities --- as
measured by its Lyapunov exponents --- are drastically reduced, indicating the
ocean's stabilizing role on the atmospheric dynamics. On decadal time scales,
the recurrence of the solution in a certain region of the invariant subspace
associated with slow modes displays some extended predictability, as reflected
by the oscillatory behavior of the error for the atmospheric variables at long
lead times.
