Wave–Wave Interaction of Unstable Baroclinic Waves

Two slightly unstable baroclinic waves in the two-layer Phillips model are allowed to interact with each other as well as the mean flow. A theory for small dissipation rates is developed to examine the role of wave–wave interaction in the dynamics of vacillation and aperiodicity in unstable systems. It is shown that the form of the dissipation mechanism as well as the overall dissipation timescale determines the nature of the dynamics. In particular, dissipation proportional to potential vorticity is shown to expunge amplitude vacillation due to wave–mean flow interactions. Wave–wave interaction, however, can yield amplitude vacillation. As the dissipation is decreased, the solutions evolve from steady waves (although propagating) to periodic vacillation until finally at small dissipation rates, chaotic behavior is obtained. This occurs in a range of relative growth rates of the two waves which depends on the strength of the wave–wave and wave–mean flow interactions