I find the idea of resonance being a cause for growth of perturbations in the atmosphere fascinating. This is quite an old idea, put forth soon after Rossby derived the dispersion relation of Rossby waves (Haurowitz, 1940), and was proposed as the mechanism behind blocking and sudden stratospheric warmings. The problem with such suggestions is that they are hard to prove from observations. More recently the idea gained popularity when Petoukhov et al (2013) came up with a diagnostic of resonance that they applied to observations, in order to study undulations in the Northern Hemisphere summer jet that accompanies extreme heat waves and floods. Their diagnositc is based on a highly simplified equivalent barotropic model of the flow. One of the main simplifications is that the midlatitude jet is a perfect waveguide, whereas in observations there is strong leaking to the tropics. In Harnik and Wirth (2024) we explore how leaking to the tropics can influence resonance in a a barotropic model. Our analysis suggests leakage weakens the amplitude growth and phase shifting across resonance, however, even quite a large degree of leakage does not preclude a spontaneous growth of the wave to a magnitude that can drive extreme events.

Current and future directions: how do other factors, like zonal asymmetry of the flow, affect resonance? 

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Haurwitz, B.: The motion of atmospheric disturbances on the spherical earth, J. Mar. Res., 3, 254–267, 1940.