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.

Nonlinear coupling among the radial, axial, and azimuthal flows in an asymmetric cold rotating plasma is considered nonperturbatively. Exact solutions describing an expanding or contracting plasma with oscillations are then obtained. It is shown that despite the flow asymmetry the energy in the radial and axial flow components can be transferred to the azimuthal component but not the vice versa, and that flow oscillations need not be accompanied by density oscillations.

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The dynamics of nonlinear two-dimensional plasma waves under non-equilibrium conditions is studied in the framework of the two-fluid hydrodynamic approach. The field of initial velocities for a twirling cylindrical plasma is considered as the initial non-equilibrium state. The influence of initial conditions on the formation and existence of nonlinear electron waves is discussed.