Abstract
It is shown that when the stability spectrum of a system has degeneracies at critical values of a control parameter, below which the system is stable or marginally stable, it may develop instabilities due to the interaction of the degenerate critical eigenmodes. When the spectrum is discrete all instabilities close to criticality are expected to stem from such degeneracies, though not all degeneracies need lead to instabilities. Two examples are briefly reviewed. the instabilities of two dimensional Stokes waves and those of an elliptical vortex.
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References
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© 1991 Springer-Verlag
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Goldhirsch, I. (1991). Spectral degeneracy and hydrodynamic stability. In: Fournier, JD., Sulem, PL. (eds) Large Scale Structures in Nonlinear Physics. Lecture Notes in Physics, vol 392. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54899-8_42
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DOI: https://doi.org/10.1007/3-540-54899-8_42
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