The two-day wave is a prevalent feature in the winds and temperatures of the middle and upper atmosphere. It is predominantly zonal wavenumber 3 but may contain wavenumbers 2-5, and the period, centered about 48 hours, may vary from 44 hours to 52 hours. Previously, the two-day wave has been explained as a manifestation of a Rossby-gravity normal mode of the atmosphere, and as a baroclinic instability of the summer easterly jet. However, recent work has revealed a third possible mechanism for the generation of the two-day wave. In this third case, the two-day wave is a result of barotropic instability in the summer subtropics. The region of barotropic instability is created by the interaction of winter hemisphere planetary waves and inertial instability in the tropics. This paper will examine the different aspects of this forcing mechanism.

The role of the inertial instability will be examined, both as the generator of the region of potential barotropic instability, and as seed noise for the growth of the instability itself. The role of the winter hemisphere planetary wave forcing will also be studied. It will be shown that while the planetary waves do not directly force the barotropic instability, they are responsible for the organization of the inertial instability, so that the zonal wavenumbers and frequencies associated with the inertial instability will be directly affected by those present in the planetary wave forcing. Differences in the nature of the forced planetary waves between the Southern and Northern hemispheres may partially account for the observed differences in the two-day wave amplitudes. The role of the background zonal wind will also be discussed briefly. The location of the critical lines for both the forced planetary waves and the two-day wave are important. The former is important for determining where the planetary waves will break and affect the mean flow, and the latter is important for determining where and if the two-day wave may develop in the region of barotropic instability. Differences in the structure of the background winds may account for the annual and seasonal variability of the two-day wave amplitude.