Linear Modes and Storm Tracks in a Two-Level Primitive Equation Model

Abstract

Linear stability analyses of three-dimensional time-mean flows in a two-level primitive equation model are presented. The model's stationary wave is generated by implementing idealized mountains at the lower boundary. Two sets of experiments are performed: the first with one mountain and the second with three mountains at equal distance from each other. Structures of streamfunctions and heat fluxes from the linearly unstable normal mode are compared with their bandpass transient counterparts in the nonlinear model simulation. The three-dimensional time-mean flow, about which the equations are linearized, is convectively unstable for both the one and three mountain cases. For the three mountain case, there is reasonable agreement between the linear mode and the bandpass transient eddies in terms of both the longitudinal location of the largest eddy amplitudes and the potential enstrophy budget, suggesting that the global mode can capture the correct structure of the climatological storm tracks for different reasons. For the one mountain case, however, the largest eddy amplitude of the linear mode extends farther downstream than that of the bandpass transient eddies. The reasonable correspondence between the linear modes and the bandpass eddies for the three mountain case appears to be due to the relative proximity of successive unstable regions. Between these successive unstable regions are diffluent flows, resulting in increased deformation and enhanced horizontal diffusion, which plays an important role in dissipating transient eddy enstrophy. It is suspected that this locally enhanced dissipation represents strained eddies by the deformation field.