Nonlinear coupling between the radial, axial, and azimuthal flows in a cold rotating plasma is considered nonperturbatively by first constructing a basis solution for a rotating flow. Simple but exact solutions that describe an expanding plasma with oscillatory flow fields are then obtained. These solutions show that the energy in the radial and axial flow components can be transferred to the azimuthal component but not the vice versa. Nonlinear electron velocity oscillations in the absence of electron density oscillations at the same frequency are shown to exist.

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