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| Titel |
Stochastic parametric resonance in shear flows |
| VerfasserIn |
F. J. Poulin, M. Scott |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 12, no. 6 ; Nr. 12, no. 6 (2005-11-03), S.871-876 |
| Datensatznummer |
250010894
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| Publikation (Nr.) |
 copernicus.org/npg-12-871-2005.pdf |
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| Zusammenfassung |
Time-periodic shear flows can give rise to Parametric Instability (PI), as in
the case of the Mathieu equation (Stoker, 1950; Nayfeh and Mook, 1995). This mechanism
results from a resonance between the oscillatory basic state and waves that
are superimposed on it. Farrell and Ioannou (1996a, b) explain that PI occurs
because the snap-shots of the velocity profile are subject to transient
growth. If the flows were purely steady the transient growth would subside
and not have any long lasting effect. However, the coupling between transient
growth and the time variation of the basic state create PI. Mathematically,
transient growth, and therefore PI, are due to the nonorthogonal eigenspace
in the linearized system.
Poulin et al. (2003) studied a time-periodic barotropic shear flow that exhibited
PI, and thereby produced mixing at the interface between Potential Vorticity
(PV) fronts. The instability led to the formation of vortices that were
stretched. A later study of an oscillatory current in the Cape Cod Bay
illustrated that PI can occur in realistic shear flows (Poulin and Flierl, 2005). These
studies assumed that the basic state was periodic with a constant frequency
and amplitude. In this work we study a shear flow similar to that found in
Poulin et al. (2003), but now where the magnitude of vorticity is a stochastic
variable. We determine that in the case of stochastic shear flows the
transient growth of perturbations of the snapshots of the basic state still
generate PI. |
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