Stable Near-Resonant States Forced by Orography in a Simple Baroclinic Model

Abstract

Stationary equilibrium states induced by orography and zonal beating are calculated in a simple non-linear quasi-geostrophic baroclinic model. For a specific vector wavenumber and for sufficiently large orography, multiple equilibrium states are found. The states are either near a resonance point in the system or are at the zonal forcing equilibrium. These multiple solutions occur because the heat transport and mountain torque are nonlinear functions of the zonal streamfunction. Near the zonal forcing equilibrium the transports are nearly zero and near the resonance point they become large enough to balance the zonal heating and friction. Only some of these near-resonant states are stable; the state at the zonal forcing equilibrium is unstable, mainly due to baroclinic instability. Near resonance, the amplitudes of the stationary eddies depend upon the strength of the zonal forcing; a stronger zonal forcing moves the solutions closer to a resonance point, which drastically increases the amplitudes of the perturbations and leaves the zonal mean quantities virtually unaffected. The solutions become more complicated when several wavenumbers and modes are considered. Some time-dependent calculations are discussed.