Current theories of zonal flow dynamics focus on the transport of poloidal momentum. Different from a cylinder, stationary poloidal flows in a tokamak are accompanied by (possibly kinetic) flows along the magnetic field, which maintain incompressibility, and comprise the major part of the flow energy. In numerical turbulence studies, the flows saturate by the turbulent diffusion of the parallel flow, whereas the poloidal momentum transport continues to strongly drive the flows.
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K. Hallatschek (2004) studied this question.
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