Dynamics of the 2-day wave in a nonlinear model of the middle and upper atmosphere

The 2-day wave is investigated in a three-dimensional model of the nonlinear primitive equations. Extending upward from the tropopause into the thermosphere, the model is forced stochastically by fluctuations of tropospheric wave structure. The behavior recovered is broadly consistent with linear calculations of the Rossby-gravity normal mode in the presence of instability. The mode's amplification depends sensitively upon details of the zonal-mean flow, which determine instability through a reversal of potential vorticity (PV) gradient. On the other hand, the mode's period and structure are robust. They retain much the same form under a variety of conditions. The response is sharply discriminated to wave number 3 and westward periods of 2.0-2.3 days, even though forcing is broadband. Under January conditions, strong easterlies and the accompanying reversal of PV gradient enable the mode to amplify through sympathetic interaction with the mean flow. The amplifying signal eventually emerges from random variability, which is excited by broadband forcing. Amplification continues until eddy velocities approach 70 m/s, whereupon the signal saturates. Horizontal mixing then ensues, destroying the meridional gradient of PV, which in turn limits instability and further amplification. Under June conditions the response fluctuates randomly during the entire integration, with no evidence of sustained amplification. Nevertheless, it too is sharply discriminated to westward periods of 2.0-2.3 days, achieving eddy velocities of 10-20 m/s. The sharply discriminated response appears even when a reversal of PV gradient is absent, leaving the mean flow stable. Under all of these conditions the structure of eddy stream function Psi' is nearly barotropic, with antisymmetric character between the hemispheres. Eddy motion assumes the form of a wave-number-3 pattern of equatorial gyres, reducing in the tropics to v' and strong cross-equatorial motion. The pattern is very similar to the limiting structure of the 2-day wave observed by UARS. Although magnified in the summer stratosphere and mesosphere, the structure of Psi' is global, with a phase reversal between the hemispheres. The modal structure extends upward into the thermosphere and, albeit weaker, as low as the tropopause.