| 27 Jun 2025
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 sres. 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.
Competing interests: At least one of the (co-)authors is a member of the editorial board of Weather and Climate Dynamics.
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Overall, this paper can be considered a companion to Harnik and Wirth (2025). While Harnik and Wirth (2025) focused on obtaining solutions for a leaky waveguide, and the effects of a leaky waveguide are somewhat analogous to wave damping, the present paper emphasizes the features of Rossby wave resonance. The authors provide a thorough review of the historical context of Rossby wave resonance in the literature, return to the linear barotropic model with pseudo-topography as forcing, derive analytical solutions, and present corresponding numerical solutions. This study suggests that, under realistic conditions, the only possible resonance solution within a linear framework corresponds to the first meridional mode.
It is a pleasure to review this paper. The main body of the manuscript is well-written and clear. I have only a few minor comments and suggestions:
Minor comments:
Overall, I found this paper to be well-structured, informative, and a valuable contribution to the literature on Rossby wave resonance. I hope the paper can be published soon.