Results are presented for the outcome of the elliptic instability, investigated by methods of dynamical-systems theory. Finite-dimensional nonlinear systems are obtained through Galerkin truncation using a systematic truncation criterion that exactly captures any fluid behavior that can also be captured via amplitude expansions. Six different regions of parameter space are explored, corresponding to linear instabilities of different symmetries and temporal types (“steady” or “oscillatory”). Four different kinds of bifurcation behavior are found among the six cases considered. One of these equilibrates at small amplitude, and the others do not, but depart significantly from the unstable equilibrium solution.
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© 1999 American Institute of Physics.
1999
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