  The main objective of this article is to study the dynamics of the stratified
rotating Boussinesq equations, which are a basic model in geophysical fluid
dynamics. First, for the case where the Prandtl number is greater than one, a
complete stability and bifurcation analysis near the first critical Rayleigh
number is carried out. Second, for the case where the Prandtl number is smaller
than one, the onset of the Hopf bifurcation near the first critical Rayleigh
number is established, leading to the existence of nontrivial periodic
solutions. The analysis is based on a newly developed bifurcation and stability
theory for nonlinear dynamical systems (both finite and infinite dimensional)
by two of the authors [16].
