Energy Transformations and Meridional Circulations associated with simple Baroclinic Waves in a two-level, Quasi-geostrophic Model

The changes in geostrophic kinetic energy predicted by the “2 – ½ dimensional” quasi-geostrophic vorticity equations without friction are shown to be compatible with the mechanical energy equation. The second-order effects on a zonal current due to the presence of very simple unstable baroclinic waves are then analysed, using a two-level model of finite lateral width without friction or heat sources. In addition to the poleward transport of sensible heat and the creation of kinetic energy by these waves, it is shown that they are accompanied in this model by a weak meridional circulation. This circulation consists of an indirect cell in middle latitudes with direct cells to the north and south. The possible importance of this mechanism in providing appropriately distributed sources and sinks of relative zonal momentum (and therefore in prescribing the distribution with latitude of the surface zonal winds) is demonstrated with the aid of Widger's observations of the horizontal momentum transfer by eddies during January 1946. Finally it is shown that about 95 per cent of the perturbation energy in the unstable waves of this type comes from the “potential energy” of the basic current, the small remainder coming from the kinetic energy of that current.