Rossby wave resonance for idealized jets on a beta-plane

Abstract. This paper analyzes Rossby wave resonance along a circumglobal midlatitude jet in the framework of the linearized inviscid barotropic vorticity equation on a zonally periodic beta-plane. Zonally symmetric Gaussian-shaped westery jets of varying amplitude and width are specified as basic states. The system is forced by pseudo-orography which varies sinusoidally in the zonal direction and which has a small meridional extent. Stationary solutions are obtained through straightforward numerical methods. The strength of resonant amplification is diagnosed by systematically varying the zonal wavenumber s, plotting the resulting wave amplitude as a function of s, and quantifying the sharpness of its peak (if existent). The numerical solutions for jet-like basic states are interpreted by reference to analytical solutions obtained for more idealized model configurations.

The analysis indicates that a jet with realistic amplitude and width may be subject to a weak form of resonance. Given that the zonal scale of a jet is much larger than its meridional scale, one may expect resonance at no more than one zonal wavenumber s_res. This resonant peak is associated with the first meridional mode, which is established through partial reflection of wave activity at the periphery of the jet flanks. The fact that a jet acts like a leaky waveguide implies that the wave amplitude remains finite even right at the resonant wavenumber. The behavior is very similar as in the classic Charney-Eliassen model, where the channel width must be chosen appropriately and where damping simulates the leakiness of the jet.