Forced and Free Meridional Circulations in the Atmosphere

The meridional variation of the sum of the non-adiabatic heating and the eddy transfer of heat, and the vertical variation of the sum of the frictional dissipation and eddy transports of zonal momentum, are shown to act as two forcing functions which produce mean meridional circulations in the atmosphere. The form and intensity of these circulations are greatly influenced by the mean temperature distribution. When the meridional temperature contrast is higher than a certain limit, these forced motions change into a more violent free convection. The criterion of this transition is obtained by a simple method and expressed in terms of a Richardson number,where Z0 is the absolute vorticity of the mean zonal flow, and c is the coefficient of friction. This condition is generally not satisfied in the atmosphere, indicating that only weak, forced, mean meridional circulation can exist. The form and intensity of the meridional circulation produced by sources of heat and momentum, and that produced by the mean non-adiabatic heating in an atmosphere at relative rest, are discussed. It is found that only a very weak, single, direct cell can be produced by the average non-adiabatic heating, with maximum meridional velocities of only a few centimeters per second. On the other hand, the effects of the horizontal eddy transport and frictional dissipation of zonal momentum tend to produce a three-cell meridional circulation in the troposphere, with a reverse cell in middle latitudes and direct cells in low and high latitudes. In the stratosphere, the circulations produced by this factor in low and middle latitudes are in the opposite sense as those in the troposphere.