HR: 16:30h
AN: OS44A-04    [Abstracts]
TI: Parametric Instability in Evolving Shear Flows
AU: * Poulin, F J
EM: fpoulin@uwaterloo.ca
AF: Francis Poulin, University of Waterloo, Waterloo, ON N2L 3G1 Canada
AB: Time-Periodic shear flows can give rise to Parametric Instability (PI), as in the case of the Mathieu equation. This mechanism results from a resonance between the oscillatory basic state and waves that are superimposed on it. Farrell and Ioannou, (1996, J. Atmos. Sci.) explain that the source of PI is that the snap-shots in time of the basic state are susceptible to transient growth. Mathematically, this is due to a linearized system that has a nonorthogonal eigenspace. Poulin, Flierl and Pedlosky (2003, J. Fluid Mech.) 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. These studies assumed that the basic state was periodic with a constant frequency. In this talk we study a shear flow similar to that found in Poulin et al., 2003 but now where the frequency is an evolving variable. This is inspired by the fact that the oscillations exhibited in this model can be generated by a travelling wave packet. If the frequency is constant the associated packet has a uniform frequency. To study the case of a wave packet we assume the frequencies change gradually in time. We determine that in these evolving shear flows the transient growth of perturbations of the snapshots of the basic state still generate PI.
DE: 4520 Eddies and mesoscale processes
DE: 4528 Fronts and jets
DE: 4568 Turbulence, diffusion, and mixing processes
SC: Ocean Sciences [OS]
MN: 2005 Joint Assembly