Brantstator, G., and I. M. Held, 1995: Westward propagating normal modes in the presence of stationary background waves. Journal of the Atmospheric Sciences, 52(2), 247-262.

Abstract: Eigenvectors and eigenvalues of the nondivergent barotropic vorticity equation linearized about zonally asymmetric wintertime mean flows are calculated to determine which barotropic modes might contribute to westward propagating disturbances observed in nature. Of particular interest are modes that correspond to a recurring pattern concentrated in the Western Hemisphere with a period of about 25 days reported by Branstator and Kushnir.

The most unstable modes of November-March means from individual years tend to be westward propogating and have a structure that is similar to the observed 25-day pattern.

By following the evolution of each Rossby-Haurwitz mode as the basic state is gradually changed from a state of rest to an observed mean state, it is demonstrated that all but about eight of the Rossby-Haurwitz modes will be modified beyond recognition by the action of the time mean flow. One of these,the second gravest antisymmetric zonal wavenumber-one mode (denoted {1,3} and sometimes referred to as the 16-day wave), has a structure that bears some resemblance to the observed 25-day pattern, but it is typically neutral. The structural similarity between this mode and the 25-day pattern is not as pronounced as the similarity between the most unstable modes and the 25-day pattern. Furthermore, the mode for the observed basic state that {1,3} evolves to depends on the path by which the resting state is transformed into the observed state, suggesting that {1,3} cannot always be thought of as a distinct mode in the presence of a realistic background. The results indicate that even if {1,3} can be considered to exist in wintertime mean flows, it is distinct from the most unstable modes on those flows. By slowly changing the basic states that support the westward propogating unstable modes until they are equal to the climatological January state that earlier studies have shown produces quasi-stationary teleconnection-like modes, it is demonstrated that the unstable westward propagating and quasi-stationary modes are related to each other.