Bifurcations in a low-order model with self-interaction

For finite the equivalent depth, the shallow-water equations (SWE) exhibit instabilities based on dyad interactions. This process is called self-interaction. In the present paper, we investigate how the stationary states of a low-order spectral model based on the SWE on the sphere are affected by self-interaction. This is done by computing the bifurcation diagram for increasing strength of the forcing in one of the vorticity components. The instabilities occurring in this low-order system are topographic instability and self-interaction. Self-interaction generates saddle-node as well as Hopf bifurcations, resulting in multiple steady-states and limit cycles. For large values of the forcing, self-intercation significantly affects the steady state curve originating from topographic instability. Extrapolating these results to the real atmosphere, self-interaction may influence the atmosphere\'s nonlinear behaviour.