Coupled cross-waves in a partially filled ‘singing wine glass’

This paper is devoted to the study of a three-resonant-eigenmode model of cross-waves excitation in a partially filled ‘singing wine glass’. This model was worked out in our previous article in detail, together with another model when only one resonant cross-wave is excited. However, our experimental studies have confirmed that it is the model with three coupled eigenmodes that applies in practice. The dynamics of three weakly coupled parametrically oscillating resonant amplitudes (for the three resonant eigenmodes) is studied in the neighbourhood of the primary subharmonic instability. Here we explain how energy from one eigenmode is transferred to another and how all three modes interact and exchange their own energy.