Planetary-Scale Flow on a Two-Layer Beta-Plane Channel Model with Topography

A two-layer low-order spectral model on a beta-plane channel with topographic, thermal and frictional forcing is designed as a compromise to resolve the relative importance and interaction of several relevant processes. The model is truncated at three zonal modes and three meridional modes. Topography forces the largest scale; the intermediate scale may be destabilized by zonal thermal forcing; the smallest scale permits barotropic scale-interaction and a rudimentary energy cascade. Multiple steady states of the simple one zonal mode and one wave mode (the 1 x 1 model) have been found. There are seven possible steady states: a zonally symmetric state, a topographically resonant state, and five baroclinic and equivalent barotropic wave states. New results emphasize relevance of the barotropic and baroclinic zonal flows; most significantly, multiple steady states exist only for a restricted range of zonal wind and vertical shear in the vicinity of the topographically resonant values. The time-dependent behavior for the 3 x 3 model is classified into six different types: zonally symmetric, steady wave state, steady propagating (Rossby wave), periodic, quasi-periodic and chaotic solutions. The regimes of the solutions for three parameters (thermal forcing, topography and friction) are investigated. The amplitude of zonal flow in wave solutions is weaker with moderate topography and is stronger with larger friction, smaller thermal forcing and higher topography or no topography. The characteristics of solutions are related to the strength of the resultant zonal flow with small or moderate topography. When the intermediate scale wave with largest meridional scale (MODE 12) is baroclinically unstable, this wave maintains the topographic wave ridge upstream of the mountain through the wave-wave interaction and also maintains other waves through form-drag; then, other modes are maintained by various mechanisms. When the topographic wave (MODE 11) becomes unstable with sufficiently large topography and small thermal forcing (but large enough to make MODE 12 baroclinically unstable), only the topographic modes exist and the other modes are dissipated by form -drag. In both cases, the mean position of MODE 11 stays to the west (upstream) of the mountain.