AN ANALYTIC STUDY OF THE BAROCLINIC ADJUSTMENT IN A QUASI-GEOSTROPHIC 2-LAYER CHANNEL MODEL

This paper reports on a study of quasi-linear baroclinic adjustment in a quasigeostrophic two-layer model with a constant baroclinic shear and an Ekman damping that is equal at the upper and lower boundaries. An analytic solution is obtained for a system consisting of a linearly unstable wave and a nontruncated zonally symmetric flow. The numerical calculations have confirmed that exclusion of the higher harmonics of an unstable wave in the analytic analysis does not alter the underlying physics of quasi-linear baroclinic adjustment. The "dynamically most efficient wave" (the wave that has the minimum equilibrated mean baroclinic shear) deduced from the analytic analysis is found to be mostly responsible for the baroclinic adjustment in the fully nonlinear model of the same baroclinic system. The dynamically most efficient wave is neither necessarily the most unstable wave nor the wave that has the largest amplitude in the fully nonlinear model. The wavelength of the most efficient wave becomes longer than that of the most unstable wave shortly after the baroclinic forcing parameter exceeds its critical value. Such a shift toward a longer wave continues as the forcing parameter increases. Thus, it is possible to predict from the analytic analysis which wave is mostly responsible for the fully nonlinear baroclinic adjustment in this two-layer model.