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    Baroclinic instability over topography : unstable at any wave number

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    Date
    2016-01-02
    Author
    Pedlosky, Joseph  Concept link
    Metadata
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    Citable URI
    https://hdl.handle.net/1912/8110
    As published
    https://doi.org/10.1357/002224016818377595
    DOI
    10.1357/002224016818377595
    Keyword
     Topography; Coastal; Coastal waves; Non linear; Slope; Wave propagation; Most unstable; Asymptotic theory; Potential vorticity 
    Abstract
    The instability of an inviscid, baroclinic vertically sheared current of uniform potential vorticity, flowing along a uniform topographic slope, becomes linearly unstable at all wave numbers if the flow is in the direction of propagation of topographic waves. The parameter region of instability in the plane of scaled topographic slope versus wave number then extends to arbitrarily large wave numbers at large slopes. The weakly nonlinear treatment of the problem reveals the existence of a nonlinear enhancement of the instability close to one of the two boundaries of this parametrically narrow unstable region. Because the domain of instability becomes exponentially narrow for large wave numbers, it is unclear how applicable the results of the asymptotic, weakly nonlinear theory are given that it must be limited to a region of small supercriticality. This question is pursued in that parameter domain through the use of a truncated model in which the approximations of weakly nonlinear theory are avoided. This more complex model demonstrates that the linearly most unstable wave in the narrow wedge in parameter space is nonlinearly stable and that the region of nonlinear destabilization is limited to a tiny region near one of the critical curves rendering both the linear and nonlinear growth essentially negligible.
    Description
    Author Posting. © Sears Foundation for Marine Research, 2016. This article is posted here by permission of Sears Foundation for Marine Research for personal use, not for redistribution. The definitive version was published in Journal of Marine Research 74 (2016): 1-19, doi:10.1357/002224016818377595.
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    • Physical Oceanography (PO)
    Suggested Citation
    Journal of Marine Research 74 (2016): 1-19
     

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