  Three-dimensional Direct Numerical Simulation (DNS) on the nonlinear dynamics
and a route to chaos in a rotating fluid subjected to lateral heating is
presented here and discussed in the context of laboratory experiments in the
baroclinic annulus. Following two previous preliminary studies by Maubert and
Randriamampianina, the fluid used is air rather than a liquid as used in all
other previous work. This study investigated a bifurcation sequence from the
axisymmetric flow to a number of complex flows. The transition sequence, on
increase of the rotation rate, from the axisymmetric solution via a steady,
fully-developed baroclinic wave to chaotic flow followed a variant of the
classical quasi-periodic bifurcation route, starting with a subcritical Hopf
and associated saddle-node bifurcation. This was followed by a sequence of two
supercritical Hopf-type bifurcations, first to an amplitude vacillation, then
to a three-frequency quasi-periodic modulated amplitude vacillation (MAV), and
finally to a chaotic<EMAIL_ADDRESS>In the context of the baroclinic annulus this
sequence is unusual as the vacillation is usually found on decrease of the
rotation rate from the steady wave flow. Further transitions of a steady wave
with a higher wave number pointed to the possibility that a barotropic
instability of the side wall boundary layers and the subsequent breakdown of
these barotropic vortices may play a role in the transition to structural
vacillation and, ultimately, geostrophic turbulence.
