Zonal flow generation by parametric instability in magnetized plasmas and geostrophic fluids

Two-dimensional magnetized plasmas and geostrophic fluids exhibit a common nonlinearity due to the advection of vorticity. It is shown here that due to this nonlinearity, the propagation of small scale wave packets is accompanied by instability of a low frequency, long wavelength component. This instability is the coherent hydrodynamic generalization of the resonant type mean flow instability identified recently [P. H. Diamond, M. N. Rosenbluth, F. L. Hinton, M. Malkov, J. Fleischer, and A. Smolyakov, 17th IAEA Fusion Energy Conference, IAEA-CN-69/TH3/1, Yokohama, 1998 (to be published, International Atomic Energy Agency, Vienna)]. The mechanism discussed here, along with the resonant type, constitutes the “hydrodynamic” and “kinetic” regimes of the same process, similar to the case of plasma-beam instabilities. It is suggested that this generic mechanism is responsible for the generation of mean flow in atmospheres of rotating planets and magnetized plasmas.