Diagnosing and analysing Rossby wave resonance along a circumglobal jetstream

A method is presented which allows one to diagnose and to analyze Rossby wave resonance along a circum-global midlatitude jet in the framework of the inviscid linear barotropic model with beta-plane geometry. Zonally symmetric Gaussian-shaped jets of varying amplitude and width are specified as a basic state. The system is forced by a pseudo-orography which varies sinusoidally in the zonal direction, and which has a very small meridional extent. Solutions are obtained through straightforward numerical methods. The strength of resonance is diagnosed by systematically varying the zonal wavenumber s, plotting the resulting wave amplitude as a function of s and quantifying the sharpness of the peak (if existent). The numerical solutions for jet-like basic states are interpreted by reference to analytical solutions obtained for more idealized model configurations

 

It is shown that a jet with realistic amplitude and width may be subject to a weak form of resonance provided that the jet is truly circum-global and there are no other forms of damping. 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 gravest meridional mode, which is established through partial reflection of wave activity at the periphery of the jet flanks. These results are reproduced well in the classic Charney-Eliassen model with an appropriate choice for the channel width. A spherical version of our diagnostic tool is expected to provide a reliable method to detect the potential for resonant amplification of Rossby waves in observed episodes