Application of Manley‐Rowe Relation in Analyzing Nonlinear Interactions Between Planetary Waves and the Solar Semidiurnal Tide During 2009 Sudden Stratospheric Warming Event

Upper mesospheric winds observed by the Svalbard specular meteor radar (16.01°E,78.16°N) are analyzed to study the tidal variabilities during the 2009 sudden stratospheric warming (SSW). We report a textbook case of nonlinear interactions between planetary waves (PWs) and the SW2 tide (SWm denotes semidiurnal westward propagating tidal mode with zonal wave number m). The Lomb‐Scargle algorithm, bispectrum, wavelet spectra, and Manley‐Rowe relations are combined to explore the frequency match, phase coherence, energy budget, and wave number relations among the interacting waves and their temporal evolution. Our results suggest that (1) 5, 10, 16 day PW normal modes interact with SW2 generating significant sidebands (S2Ss) at frequencies lower and higher than SW2, known as SW1 and SW3 enhancements, respectively; (2) SW2 is the main energy supplier for both SW1 and SW3, hence shrinks in the interactions; (3) whereas the PWs export relatively negligible energy to SW3 but accept energy from SW2 in generating SW1, therefore, the PWs is not subject to the interactions but controlled by external dynamics, which might in turn act as a key in switching on/off the SW1 and SW3 interactions independently; (4) the SW1 enhancement could be explained as a byproduct of the planetary wave amplification by stimulated tidal decay (PASTIDE); (5) PASTIDE contributes energy to the secondary PW in the late SSW stage reported in previous studies; and (6) one SW1 component associated with the 16 day PW is very close to the semidiurnal lunar mode in frequency, which might contaminate the estimation of the lunar tidal amplification in previous studies. Plain Language Summary Nonlinear interaction is a prototypical behavior of waves, as fundamental as Doppler shift, interference, and diffraction. Nonlinear interactions between atmospheric planetary scale waves have been reported in numerous studies. In the current work, we apply for the first time Manley‐Rowe relations to determine the energy flow in the atmospheric interactions and roles of the interacting waves. Particularly, we report and analyze a textbook case of nonlinear interactions between planetary waves (PWs) and the migrating solar semidiurnal tide. Our analysis suggests that the secondary waves, well known as zonal wave 1 and wave 3 enhancements, are fed on the energy mainly from the tide. Although the energy flow through PWs is relatively negligible, our investigations suggest that the energy budget of PWs might act as a