NONLINEAR BAROCLINIC ADJUSTMENT AND WAVE-NUMBER SELECTION IN A SIMPLECASE

The process of baroclinic equilibration in the atmosphere is investiga ted using a high-resolution two-layer quasigeostrophic model in a beta -plane channel. One simple channel geometry is investigated for which only two zonal waves are initially unstable, with the shorter being li nearly more unstable bur nonlinearly less effective. It is discovered that the mechanism of nonlinear baroclinic adjustment, formerly propos ed by Cehelsky and Tung, including a nonlinear wavenumber selection pr ocess, can explain the equilibration at all levels of forcing for this case. At small forcings the most unstable wave dominates the heat flu x, consistent with the quasi-linear equilibration of Stone's simple ba roclinic adjustment. At high forcings the longer, less unstable wave d ominates, land the equilibration involves both quasi-linear dynamics b y this dominant wave and nonlinear transfer from the shorter to the lo nger wave. For intermediate forcings there is a transition between the low and high regimes; no single wave dominates. At every forcing exce pt in the intermediate regime there is critical equilibration by the d ominant wave. For intermediate forcings, the model equilibrates at a v alue between the critical shear of the two waves. The wavenumber selec tion process involves a threshold of heat transport for each wave. Abo ve this, the amplitude of the wave would be so large as to cause itsel f to break and saturate. The shorter wave's threshold occurs at modera te forcings, at which point it relinquishes dominance to the longer wa ve. A method for calculating these thresholds is proposed, which invol ves only robust features of the equilibrium.