The instability of finite amplitude rossby waves on the infinite beta-plane

The normal mode instability problem for a stationary Rossby wave of finite amplitude and arbitrary orientation is examined on the infinite beta-plane using a Floquet technique. A survey of the instability problem as a function of the basic state wave amplitude and wave orientation is presented. In the large amplitude case, two modes of instability are found, while in the small amplitude case, a family of resonant interactions can completely describe the Floquet results. For intermediate values of amplitude, a combination of the large and small amplitude limits can explain the instabilities. For the range of greatest geophysical interest, two physically distinct unstable modes of approximately equal growth rate are available for certain values of the basic state wave orientation. Relevance to geophysical flows and the instability problem on the sphere are discussed briefly.