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Barotropic instability of coastal flows as a boundary-value problem: linear and non-linear theory.

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Title: Barotropic instability of coastal flows as a boundary-value problem: linear and non-linear theory.
Authors: WILLMOTT, ANDREW J.1 ajwil@pol.ac.uk, CUSHMAN-ROISIN, BENOIT2
Source: Geophysical & Astrophysical Fluid Dynamics. Aug2009, Vol. 103 Issue 4, p279-292. 14p. 1 Diagram, 2 Charts, 3 Graphs.
Subjects: Boundary value problems, Complex variables, Astronomical perturbation, Whirlwinds, Dynamic meteorology, Territorial waters, Continental shelf
Abstract: The barotropic instability is traditionally viewed as an initial-value problem wherein wave perturbations of a laterally sheared flow in a homogeneous uniformly rotating fluid that temporally grows into vortices. The vortices are capable of mixing fluid on the continental shelf with fluid above the continental slope and adjacent deep-sea region. However, the instability can also be viewed as a boundary-value problem. For example, a laterally sheared coastal flow is perturbed at some location, creating perturbations that grow spatially downstream. This process leads to a time periodic flow that exhibits instability in space. This article first examines the linear barotropic instability problem with real frequency and complex wavenumber. It is shown that there exists a frequency band within which a spatially growing wave is present. It is then postulated that far downstream the spatially unstable flow emerges into a chain of identically axisymmetric vortices. Conservation of mass, momentum and energy fluxes are applied to determine the diameter, spacing and the speed of translation of the vortices. [ABSTRACT FROM AUTHOR]
Copyright of Geophysical & Astrophysical Fluid Dynamics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Barotropic instability of coastal flows as a boundary-value problem: linear and non-linear theory.
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  Data: <searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Complex+variables%22">Complex variables</searchLink><br /><searchLink fieldCode="DE" term="%22Astronomical+perturbation%22">Astronomical perturbation</searchLink><br /><searchLink fieldCode="DE" term="%22Whirlwinds%22">Whirlwinds</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamic+meteorology%22">Dynamic meteorology</searchLink><br /><searchLink fieldCode="DE" term="%22Territorial+waters%22">Territorial waters</searchLink><br /><searchLink fieldCode="DE" term="%22Continental+shelf%22">Continental shelf</searchLink>
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  Data: The barotropic instability is traditionally viewed as an initial-value problem wherein wave perturbations of a laterally sheared flow in a homogeneous uniformly rotating fluid that temporally grows into vortices. The vortices are capable of mixing fluid on the continental shelf with fluid above the continental slope and adjacent deep-sea region. However, the instability can also be viewed as a boundary-value problem. For example, a laterally sheared coastal flow is perturbed at some location, creating perturbations that grow spatially downstream. This process leads to a time periodic flow that exhibits instability in space. This article first examines the linear barotropic instability problem with real frequency and complex wavenumber. It is shown that there exists a frequency band within which a spatially growing wave is present. It is then postulated that far downstream the spatially unstable flow emerges into a chain of identically axisymmetric vortices. Conservation of mass, momentum and energy fluxes are applied to determine the diameter, spacing and the speed of translation of the vortices. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Group: Ab
  Data: <i>Copyright of Geophysical & Astrophysical Fluid Dynamics is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1080/03091920802604648
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 279
    Subjects:
      – SubjectFull: Boundary value problems
        Type: general
      – SubjectFull: Complex variables
        Type: general
      – SubjectFull: Astronomical perturbation
        Type: general
      – SubjectFull: Whirlwinds
        Type: general
      – SubjectFull: Dynamic meteorology
        Type: general
      – SubjectFull: Territorial waters
        Type: general
      – SubjectFull: Continental shelf
        Type: general
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      – TitleFull: Barotropic instability of coastal flows as a boundary-value problem: linear and non-linear theory.
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              M: 08
              Text: Aug2009
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              Y: 2009
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