Nonlinear Baroclinic Adjustment and Wavenumber Selection in a Simple Case

The process of baroclinic equilibration in the atmosphere is investigated using a high-resolution two-layer quasigeostrophic model in a b-plane channel. One simple channel geometry is investigated for which only two zonal waves are initially unstable, with the shorter being linearly more unstable but nonlinearly less effective. It is discovered that the mechanism of nonlinear baroclinic adjustment, formerly proposed by Cehelsky and Tung, including a nonlinear wavenumber selection process, can explain the equilibration at all levels of forcing for this case. At small forcings the most unstable wave dominates the heat flux, consistent with the quasi-linear equilibration of Stone’s simple baroclinic adjustment. At high forcings the longer, less unstable wave dominates, and the equilibration involves both quasi-linear dynamics by this dominant wave and nonlinear transfer from the shorter to the longer wave. For intermediate forcings there is a transition between the low and high regimes; no single wave dominates. At every forcing except in the intermediate regime there is critical equilibration by the dominant wave. For intermediate forcings, the model equilibrates at a value between the critical shear of the two waves. The wavenumber selection process involves a threshold of heat transport for each wave. Above this, the amplitude of the wave would be so large as to cause itself to break and saturate. The shorter wave’s threshold occurs at moderate forcings, at which point it relinquishes dominance to the longer wave. A method for calculating these thresholds is proposed, which involves only robust features of the equilibrium.