Amplification of the 2‐day wave from mutual interaction of global Rossby‐gravity and local modes in the summer mesosphere

The 2‐day wave is a planetary‐scale wave recurrently observed in the summer mesosphere. It is predominantly zonal wave number 3 (though wave numbers 2 and 4 are also observed) and has a period of approximately 2 days. It is generally accepted that the 2‐day wave has characteristics of both global‐scale Rossby‐gravity normal mode and baroclinic/barotropic instability. Here we examine how local instability amplifies the global Rossby‐gravity mode. We perform a two‐dimensional instability calculation to calculate unstable modes. The fastest growing modes have wave number 3, a 35‐hour Rossby mode localized in the summer hemisphere at high latitudes, and a Rossby‐gravity mode with period 42 hours with similar characteristics to the observed 2‐day wave. The Rossby‐gravity mode was examined as the background state was changed from an isothermal atmosphere to realistic conditions. The wave was slowly Doppler shifted toward shorter periods and its spatial structure became distorted. Approaching realistic conditions the mode becomes weakly unstable. Near this point a localized Rossby mode also emerges which exists on the reversed potential vorticity gradients of the summer jet. This has the necessary characteristics to phase lock with the Rossby‐gravity mode. Hence we propose that the 2‐day wave amplifies from the interaction of global‐scale Rossby‐gravity and local modes. A nonlinear model was used to examine the unstable modes as they grow to finite amplitude. It was found that even though the 35‐hour Rossby wave had the largest growth rates, it did not reach large amplitude. It was the slower growing 42‐hour Rossby‐gravity mode which dominated the long time evolution.