Barotropic instability of zonally varying flow forced by multimode topography

Abstract

Abstract The linear stability characteristics of zonally varying basic flow forced by multimode topography are investigated with a quasigeostrophic, barotropic model on an infinite β-plane. Ekman pumping is the sole dissipative process. The topography is chosen to vary from one to five zonal modes, with the amplitudes chosen to be representative of those at middle latitudes in the Northern Hemisphere. The stability analysis reveals two distinct types of most unstable disturbances: (1) a nearly stationary instability (NSI) that is associated with basic flows near topographic resonance, a parameter setting where a single mode dominates the basic state; (2) a low frequency instability (LFI) that occurs for basic flows dominated by at least two forced waves of similar amplitude. The NSI (LFI) are characterized by relatively large (small) growth rates which are (in)sensitive to small changes in the basic flow. The importance of topographic resolution and disturbance-topography interaction on the stability of the system are also examined. It is shown that multimode topography is solely responsible for generating unstable basic flows in regions of parameter space where single mode basic states are stable. The interaction of the disturbance with topography is most important for those flows where planetary vorticity advection approximately matches the advection of disturbance relative vorticity. Arbitrarily excluding disturbance-topography interaction eliminates the LFI and results in an overestimate of the range of NSI. The weakly non-linear equilibration of the system is also briefly discussed.