Rossby wave second harmonic generation observed in the middle atmosphere.

Second harmonic generation is the lowest-order wave-wave nonlinear interaction occurring in, e.g., optical, radio, and magnetohydrodynamic systems. As a prototype behavior of waves, second harmonic generation is used broadly, e.g., for doubling Laser frequency. Second harmonic generation of Rossby waves has long been believed to be a mechanism of high-frequency Rossby wave generation via cascade from low-frequency waves. Here, we report the observation of a Rossby wave second harmonic generation event in the atmosphere. We diagnose signatures of two transient waves at periods of 16 and 8 days in the terrestrial middle atmosphere, using meteor-radar wind observations over the European and Asian sectors during winter 2018-2019. Their temporal evolution, frequency and wavenumber relations, and phase couplings revealed by bicoherence and biphase analyses demonstrate that the 16-day signature is an atmospheric manifestation of a Rossby wave normal mode, and its second harmonic generation gives rise to the 8-day signature. Our finding confirms the theoretically-anticipated Rossby wave nonlinearity.