SECONDARY INSTABILITY, EOF REDUCTION, AND THE TRANSITION TO BAROCLINIC CHAOS

High-resolution numerical simulations illustrate how an initial barocl inic instability may become chaotic as the degree of supercriticality is increased. The route to chaos is via bifurcations to periodic and q uasi-periodic states, but the spatial structures involved are much mor e complex than those assumed in previous low-order models. The fundame ntal participants in the transition can be educed by studying the symm etry-breaking secondary instabilities of fixed points of the primary b aroclinic instability problem. These unstable disturbances to the equi librium wavy baroclinic flow serve to eradicate the fundamental symmet ries of the classic two-layer baroclinic instability problem with equa l layer depths and cross-stream-symmetric zonal currents. Reduced low- dimensional models that replicate the full 10(4)-mode computer simulat ions can be formulated by projecting the governing equations onto the EOFs (empirical orthogonal functions) of the large-scale calculations. The successful construction of such models using relatively few EOFs appears to be related to the fact that the EOFs are almost identical t o the secondary instabilities of the primary baroclinic wave state, an d these secondary instabilities are, in turn, the primary participants in the supercritical periodic and quasiperiodic states.