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# [AAS11-06] Formation of two dimensional and three dimensional circulation responding to unsteady wave forcing in the middle atmosphere

Keywords:middle atmosphere, circulation, wave forcing

As large-scale atmospheric response to the forcing can be described as a linear response, the method of Green’s function, which is a response to the delta function, is one of useful approaches for analysis of the linear response to forcing. By using the Green's function method, we mainly examine the response to a wave forcing in the zonal momentum equation.

First, we investigate the response to the zonally-uniform forcing. The steady solution of the meridional circulation responding to a constant forcing is composed of two cells in the vertical. For a forcing with a shaped of the step function in time, gravity waves are radiated as a transient response, and a meridional circulation with an inertial oscillation finally remains. The quasi-steady meridional circulation accords well with the steady state solution for a constant forcing. The time scale needed for the formation of the meridional circulation depends on the aspect ratio of the wave forcing structure, as is consistent with a theoretical expectation. In addition, it is shown that the group velocity of gravity waves and the spatial scale of the forcing determine the time scale of the circulation formation. We also investigate the case for the forcing which changes gradually in time. When the forcing time change is slower than the inertial period, the meridional circulation always accords with that estimated using the “steady-state assumption”. The distribution ratio of the wave forcing to the zonal-wind acceleration and the Coriolis torque is also investigated. The distribution ratio is determined by the shape of the wave forcing and explained by the dimensional analysis.

Second, we investigate the response to zonally-nonuniform forcing. In this case, it is expected that Rossby waves are radiated as transient response because of beta effect. So as to focus only on the Rossby wave response, governing equations are derived following the method of balance equations used by Leith (1980). For the steady forcing case with beta effect, the geostrophic flow becomes zonally asymmetric and has large magnitudes to the west of the forcing. For the step-function forcing, Rossby waves are radiated as a transient response. Rossby waves having smaller zonal wave numbers radiated faster from the forcing region. Time period needed to reach the steady state depends strongly on the strength of the linear relaxation.