[1] Understanding periods associated with climate variations has been challenging and has attracted scientific study. In the work presented here, we establish a theoretical dynamical model driven by Sun-Moon gravitation (SMG) and present basic SMG wave characteristics and SMG-induced nonlinear motions for geophysical fluids. As compared to observations, waves and motions demonstrate climate variations associated with abundant structures and climatic rhythms, including the 30-60 day oscillation, seasonality, El Niño-Southern Oscillation-like interannual variation, etc. In our work, periods depended upon the obliquity and revolution velocity of the Sun and Moon; the speed of geophysical fluids; and the latitude, radius, and rotation velocity of Earth. The rotation of Earth helps fluids remember and accumulate momentum in geophysical fluids that are provided by the SMG on multiple time scales, which may contribute to multiperiods of climate oscillations. The speed-dependent periods of SMG-induced flow are of a broad spectrum (i.e., faster speeds, shorter periods). SMG-induced flow in an atmosphere of faster flow tends to have shorter (e.g., seasonal and annual) periods, while an ocean of slower flow tends to have longer (e.g., annual and interannual) periods.

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