Precession resonance of Rossby wave triads and the generation of low-frequency atmospheric oscillations

Abstract

The dynamics of the Earth's atmosphere is characterized by a wide spectrum of oscillations, ranging from hourly to interdecadal and beyond. The low frequency component of the atmospheric variability cannot be understood solely in terms of linear atmospheric waves that have shorter timescales. A newly proposed mechanism, the precession resonance mechanism, is a regime of highly efficient energy transfer in the spectral space in turbulent systems. Here, we investigate the role of the precession resonance, and the alignment of dynamical phases, in the generation of low frequency oscillations and the redistribution of energy/enstrophy in the spectral space using the barotropic vorticity equation. First, the mechanism and its ability to generate low frequency oscillations are demonstrated in low-order models consisting of four and five nonlinearly interacting Rossby-Haurwitz waves. The precession resonance onset is also investigated in the full barotropic vorticity equation, and the results are in agreement with the reduced models. Efficiency peaks in the energy/enstrophy transfer also correspond to regimes of strong excitation of low frequency oscillations. The results suggest that the organization of the dynamical phases plays a key role in the redistribution of energy in the spectral space, as well as the generation of low frequencies in the barotropic vorticity equation.

Rieger, Schwabe, Suess-de Vries: The Sunny Beats of Resonance

“…In this respect, our line of argument is quite similar to that of Raphaldini et al (2019Raphaldini et al ( , 2022, who also tried to explain, first, the Schwabe cycle in terms of nonlinear triads of magneto-Rossby waves with a ten times shorter time scale, and, second, the Gleissberg and Suess-de Vries cycles as higher-order "precession resonances", including two such triads. In contrast to these works, however, we focused here on the very specific 11.07-year period that shows up in the nonlinear interaction of three tidally induced magneto-Rossby waves.…”

“…Again, our focus was on a sharp 193-year beat period (as indeed observed by Prasad et al, 2004) rather than on some broad signal on the general 100 -200-year scale. That said, we believe that the mathematical framework of triadic (and "precession") interactions as developed by Raphaldini et al (2019Raphaldini et al ( , 2022, together with the methods to derive the α-effect for Rossby waves Avalos-Zuñiga, Plunian, and Rädler (2009), represent an ideal starting point for more quantitative corroborations of the ideas that could only be sketched in this paper. Complementarily to this focus on the α-effect, we might also evaluate the nonlinear energy transfer terms from the Appendix of Dikpati et al (2018), which, via tachocline nonlinear oscillations, may lead to a similar -related synchronization mechanism as once proposed by Zaqarashvili (1997).…”

“…In contrast to these works, however, we focused here on the very specific 11.07-year period that shows up in the nonlinear interaction of three tidally induced magneto-Rossby waves. A second difference applies to the transition from Rieger, via Schwabe, to Suess-de Vries, for which, in our opinion, the argument of Raphaldini et al (2022) may run into conceptual problems due to the intervening oscillatory dynamo field, which changes "on-the-fly" the eigenfrequencies of the underlying magneto-Rossby waves.…”

“…Two types of such nonlinear wave couplings were recently studied in detail by Raphaldini et al (2019Raphaldini et al ( , 2022. In either case, they involve quadratic interactions between the waves, which might lead to various frequency and wavenumber resonances.…”

Intermittency Scaling for Mixing and Dissipation in Rotating Stratified Turbulence at the Edge of Instability

“…Extreme events are observed frequently in the atmosphere, e.g., in terms of w, θ [88], of the rate of energy dissipation [89] as well as for extreme precipitation [90,91]. A possible role in the formation of such structures is through the precession resonance of Rossby waves which was analyzed e.g., in [92,93], leading to their breaking as well as to their interactions with potential vorticity [94,95]. Similarly, in the ocean, wave breaking leads to efficient mixing processes [77][78][79], and observations of double-signed skewness can be the signature of a front, modeled in a dichotomic way for relative vorticity [67] as for the Agulhas current.…”