Resonant Forcing of Oceanic and Atmospheric Rossby Waves in (Sub) Harmonic Modes: El Niño, Glacial Cycles, Extreme Rain and Heat Events

Baroclinic wave resonance, particularly Rossby waves, has attracted great interest in ocean and atmospheric physics since the 1950s. Research on Rossby wave resonance co-vers a wide variety of phenomena that can be unified when focusing on quasi-stationary Rossby waves traveling at the interface of two stratified fluids. This assumes a clear dif-ferentiation of the pycnocline where the density varies strongly vertically. In the atmos-phere, such stationary Rossby waves are observable at the tropopause, at the interface be-tween the polar jet and the ascending air column at the meeting of the polar and Ferrel cell circulation or between the subtropical jet and the descending air column at the meeting of the Ferrel and Hadley cell circulation. The movement of these air columns varies accord-ing to the declination of the Sun. In the oceans, quasi-stationary Rossby waves are ob-servable in the tropics, at mid-latitudes, and around the subtropical gyres (i.e. the gyral Rossby waves GRWs) due to the buoyant properties of warm waters originating from tropical oceans, transported to high latitudes by western boundary currents. The thermo-cline oscillation results from solar irradiance variations induced by the Sun's declination, as well as solar and orbital cycles. It is governed by the forced, linear, inviscid shallow water equations on the β-plane (or β-cone for GRWs), namely the momentum, continuity and potential vorticity equations. The coupling of multi-frequency wave systems occurs in exchange zones. Here, the geostrophic forces reflecting the superposition of zonal/polar and meridional/radial currents of the waves perturb the geo-strophic balance of the basin. Here, it is shown that the ubiquity of resonant forcing in (sub)harmonic modes of Rossby waves in stratified media results from two properties: 1) the natural period of Rossby wave systems tunes to the forcing period - 2) the restoring forces between the different multi-frequency Rossby waves assimilated to inertial Caldirola-Kanai (CK) oscillators are all the stronger as the perturbations of the geostrophic equilibrium in the exchange zones are more significant. According to the CK equations, this resonance mode ensures the sustainability of the wave systems despite the variability of the forcing periods. The reso-nant forcing of quasi-stationary Rossby waves is at the origin of climate variations as well-known as El Niño, glacial-interglacial cycles or extreme events generated by cold drops or, conversely, heat waves. This approach attempts to provide some new avenues for addressing climate and weather issues. Some of these aim to better account for the cli-mate's response to anthropogenic warming.