Resonant interaction of Rossby waves in two-dimensional flow on a ββ plane

An incompressible two-dimensional flow on a ββ plane is considered. Rossby waves are generally expected to dominate the ββ plane dynamics, and here in this paper we prove a mathematically rigorous theorem: that at a high ββ, the flow dynamics is governed exclusively by the resonant interactions of Rossby waves.

► We study an incompressible flow on a ββ plane with periodic initial data. ► We prove a theorem rigorously. ► The theorem shows that the flow is dominated by the resonance of the Rossby waves.