On the multiplicity of equilibria of baroclinic waves

It is shown that, including the null solution (the Hadley state), there can be six different equilibria in a quasi-geostrophic forced dissipative β-plane channel model of a triadic baroclinic wave system. The dependence of the structural, energetics, and stability properties of each equilibrium solution upon the forcing and dissipation parameters have been delineated. Furthermore, the fairly subtle relations among these equilibria have been uniquely identified on the basis of the local bifurcation theory.

Analytic solutions for the viscous single-wave equilibria are obtained. They are unique in contrast to those under an inviscid condition. The latter additionally depend upon the initial state. The diagnosis of the physical character of the single-wave equilibria reveals that such a wave is dynamically neutral with respect to the modified zonal flow. It has identical structural properties as those of a neutral wave according to the linear instability theory.

Two distinctly different classes of multiple-wave equilibria are found numerically. One class is essentially a modified form of the single-wave equilibria. The other class uniquely stems from the presence of wave-wave interaction. A stable single-wave equilibrium and a stable multiple-wave equilibrium are found to coexist in a small part of the parameter domain. The instability of the multiple wave equilibria would result in triad-limit-cycles in this model as previously reported by Mak.