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The current study focuses on dynamics and evolution of large-scale motions in a turbulent Rayleigh-Bénard convection in a cylindrical domain with a moderate aspect ratio of 6.3. We perform Direct Numerical Simulations of the problem with a spectral-element code, and analyze the temporal dynamics of the azimuthal Fourier modes associated with the large-scale motions. Focusing on the first several modes, we document the processes that govern their evolution and interactions, including the in-mode processes, such as fast and slow rotations, as well as inter-mode interactions associated with the mode cessations and transitions. Time scales associated with these processes are analyzed.