Complex dynamics of the vertical oscillating and stably stratified square cavity

We study numerically the behavior of a fluid flow inside the vertically oscillating and stably stratified square cavity.  For a set of harmonic forcing frequencies and amplitudes, it is well known that the flow's basic state loses stability to a nontrivial internal wave mode.  However, the dynamical details of how the instability occurs are not well understood.  The dynamics are shown to be complicated by a family of codimension-two bifurcations near the primary locus of instability.