  (abridged) Aims: We present new results exhibiting a subcritical baroclinic
instability (SBI) in local shearing box models. We describe the 2D and 3D
behaviour of this instability using numerical simulations and we present a
simple analytical model describing the underlying physical process.
  Results: A subcritical baroclinic instability is observed in flows stable for
the Solberg-Hoiland criterion using local simulations. This instability is
found to be a nonlinear (or subcritical) instability, which cannot be described
by ordinary linear approaches. It requires a radial entropy gradient weakly
unstable for the Schwartzchild criterion and a strong thermal diffusivity (or
equivalently a short cooling time). In compressible simulations, the
instability produces density waves which transport angular momentum outward
with typically alpha<3e-3, the exact value depending on the background
temperature profile. Finally, the instability survives in 3D, vortex cores
becoming turbulent due to parametric instabilities.
  Conclusions: The subcritical baroclinic instability is a robust phenomenon,
which can be captured using local simulations. The instability survives in 3D
thanks to a balance between the 2D SBI and 3D parametric instabilities.
Finally, this instability can lead to a weak outward transport of angular
momentum, due to the generation of density waves by the vortices.
