Generalized stability theory. Part II: Nonautonomous Operators
- Harvard Univ., Cambridge, MA (United States)
An extension of classical stability theory to address the stability of perturbations to time-dependent systems is described. Nonnormality is found to play a central role in determining the stability of systems governed by nonautonomous operators associated with time-dependent systems. This pivotal role of nonnormality provides a conceptual bridge by which the generalized stability theory developed for analysis of autonomous operators can be extended naturally to nonautonomous operators. It has been shown that nonnormality leads to transient growth in autonomous systems, and this result can be extended to show further that time-dependent nonnormality of nonautonomous operators is capable of sustaining this transient growth leading to asymptotic instability. This general destablizing effect associated with the time dependence of the operator is explored by analyzing parametric instability in periodic and aperiodic time-dependent operators. Simple dynamical systems are used as examples including the parametrically destabilized harmonic oscillator, growth of errors in the Lorenz system, and the asymptotic destabilization of the quasigeostrophic three-layer model by stochastic vacillation of the zonal wind. 39 refs., 9 figs.
- DOE Contract Number:
- FC03-90ER61010
- OSTI ID:
- 457945
- Journal Information:
- Journal of the Atmospheric Sciences, Journal Name: Journal of the Atmospheric Sciences Journal Issue: 14 Vol. 53; ISSN 0022-4928; ISSN JAHSAK
- Country of Publication:
- United States
- Language:
- English
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