Formation of Two-Dimensional Circulation in Response to Unsteady Wave Forcing in the Middle Atmosphere

Abstract

In previous studies, a steady-state assumption has been frequently used for the analysis of wave-induced meridional circulation. In general, however, the wave forcing is not constant and thus induced circulation can vary in time. Thus, to understand such transient behaviors, time evolutions of a slow variable describing balanced flows and two fast variables describing gravity waves and flows that are slaved to balanced flows are investigated. A Boussinesq equation system is used to examine zonal-mean flow responses to unsteady zonally uniform forcing. Green’s function is used to analytically obtain the evolution of meridional circulation. Responses to zonal wave forcing are mainly examined although responses to a diabatic heating and to wave forcing are discussed in brief. For forcing with a step function shape in time, gravity waves are radiated as a transient response. The time needed to form the circulation depends on the aspect ratio (i.e., latitudinal to vertical lengths) of wave forcing, which determines the group velocity of gravity waves. When the forcing time scale is longer than the inertial period, the response does not include gravity wave radiation and mainly involves a meridional circulation, which is similar to the solution for steady forcing. The two-celled meridional circulation describes the early stage response to the forcing and can be used to examine how the wave forcing is distributed to zonal wind acceleration and Coriolis torque. It is shown that the distribution depends on the aspect ratio of the forcing.