Rossby wave resonance for idealized jets on a beta-plane : towards a better understanding of the meridional wave structure

Abstract

The paper discusses a novel method to diagnose and investigate Rossby wave resonance along a circumglobal midlatitude jet with particular focus on the meridional wave structure. As a framework, the linearized inviscid barotropic vorticity equation is considered on a zonally periodic beta-plane. Zonally symmetric Gaussian-shaped westerly jets of varying amplitude and width are specified as basic states. The system is forced by pseudo-orography with small meridional extent, being located at jet latitude and varying sinusoidally in the zonal direction. 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 the jet is much larger than its meridional scale, one may expect resonance at no more than one zonal wavenumber sres. The single 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 leakiness of the waveguide implies that the wave amplitude remains finite at the resonant wavenumber even for inviscid wave dynamics. 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.