With certain exceptions such as the ACC and flows around submarine plateaux, strong currents in the ocean are usually non-rentrant. They typically have lengths that are only a few times the maximally growing wavelengths predicted by quasigeostrophic instability theory for infinitely long jets with a similar cross-stream profile. The growth of meanders on "short" currents such as the Gulf Stream Extension or Kuroshio Extension is therefore very sensitive to the nature of small disturbances away from the jet, particularly upstream. Such sensitivity has important consequences for the design of observational strategies aimed at improving understanding of jet meandering.
We apply the tool of non-normal stability theory to a simple quasigeostrophic model of a flow that contains a mid-latitude jet formed by the separation of a western boundary current. The most rapidly growing singular vectors, determined using optimization times ranging from 3 to 100 days, can be split into several classes. Some are associated with shifts in the separation point, some with disturbances in the attached western boundary currents upstream, some with disturbances in the recirculations that border the separated jet, and some with perturbations to the path of the separated jet. Significant transient growth can occur even when the circulation being perturbed is in a "stable" steady state. The structures of the dominant singular vectors vary with optimization time, the Reynolds number of the flow, and the state of the flow. We also compare the singular vectors of the evolving flow with singular vectors of short and long term means of the flow and compare the fluctuations around the mean with the singular and Lyapunov vectors computed from the mean. A crude estimate of the likelihood of optimal excitation is obtained by Monte-Carlo techniques. Finally, ensembles of random initial perturbations to a developed jet are evolved forwards over the same optimization times used in the computation of the singular vectors and various moments of the final states in the ensemble are compared to the Lyapunov vectors.
This work has been supported by the Office of Naval Research.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics