Abstract
An exact solution of the nonlinear magnetohydrodynamic equations for a viscous incompressible fluid of finite conductivity is obtained, which represents a circularly polarized structure with time dependent amplitude in a uniform magnetic field. There is a phase difference of ½π between the spatial structures of the velocity and the magnetic field of the disturbance. In the inviscid perfectly conducting limit, this solution represents a standing helical oscillation which is a circularly polarized standing Alfvén wave of arbitrary amplitude, and the sum of the kinetic and magnetic energy densities of the oscillation are constant in the absence of any input of energy.
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