Double Hopf bifurcations in the quasigeostrophic potential vorticity equations

摘要

We analyze the bifurcations that occur in a simple baroclinic flow described by the two layer quasigeostrophic potential vorticity equations. In particular, we study the solutions that bifurcate from a steady solution (basic state) that can become unstable due to both baroclinic and barotropic sources. It is found that, via Hopf bifurcation, travelling waves of various wave numbers can equilibrate when the steady solution becomes unstable. Furthermore, there are points in the space of control parameters where double Hopf bifurcations occur. Near these points, the nonlinear interaction of two travelling wave solutions is analyzed.