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  • Delay coordinate embedding  (1)
  • invariant manifold  (1)
  • 1
    Publication Date: 2022-05-26
    Description: Author Posting. © American Geophysical Union, 2004. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 109 (2004): C08002, doi:10.1029/2003JC002148.
    Description: This study establishes a series of tests to examine the relative utility of nonlinear time series analysis for oceanic data. The performance of linear autoregressive models and nonlinear delay coordinate embedding methods are compared for three numerical and two observational data sets. The two observational data sets are (1) an hourly near-bottom pressure time series from the South Atlantic Bight and (2) an hourly current-meter time series from the Middle Atlantic Bight (MAB). The nonlinear methods give significantly better predictions than the linear methods when the underlying dynamics have low dimensionality. When the dimensionality is high, the utility of nonlinear methods is limited by the length and quality of the time series. On the application side we mainly focus on the MAB data set. We find that the slope velocities are much less predictable than shelf velocities. Predictability on the slope after several hours is no better than the statistical mean. On the other hand, significant predictability of shelf velocities can be obtained for up to at least 12 hours.
    Description: This research was supported by Office of Naval Research grants N00014-01-1-0260, N00014-92-J-1481, and N10014-99-1-0258.
    Keywords: Predictability ; Delay coordinate embedding ; Shelf break
    Repository Name: Woods Hole Open Access Server
    Type: Article
    Format: application/pdf
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of nonlinear science 5 (1995), S. 337-358 
    ISSN: 1432-1467
    Keywords: settling of aerosol particles ; singular perturbation ; invariant manifold ; heteroclinic break-up ; symmetric map
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Summary This paper presents a proof that given a dilute concentration of aerosol particles in an infinite, periodic, cellular flow field, arbitrarily small inertial effects are sufficient to induce almost all particles to settle. It is shown that when inertia is taken as a small parameter, the equations of particle motion admit a slow manifold that is globally attracting. The proof proceeds by analyzing the motion on this slow manifold, wherein the flow is a small perturbation of the equation governing the motion of fluid particles. The perturbation is supplied by the inertia, which here occurs as a regular parameter. Further, it is shown that settling particles approach a finite number of attracting periodic paths. The structure of the set of attracting paths, including the nature of possible bifurcations of these paths and the resulting stability changes, is examined via a symmetric one-dimensional map derived from the flow.
    Type of Medium: Electronic Resource
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