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    Oceanic internal-wave field : theory of scale-invariant spectra

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    2010jpo4132.1.pdf (767.6Kb)
    Date
    2010-12
    Author
    Lvov, Yuri V.  Concept link
    Polzin, Kurt L.  Concept link
    Tabak, Esteban G.  Concept link
    Yokoyama, Naoto  Concept link
    Metadata
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    Citable URI
    https://hdl.handle.net/1912/4343
    As published
    https://doi.org/10.1175/2010JPO4132.1
    DOI
    10.1175/2010JPO4132.1
    Keyword
     Waves; Oceanic; Internal waves; Spectral analysis 
    Abstract
    Steady scale-invariant solutions of a kinetic equation describing the statistics of oceanic internal gravity waves based on wave turbulence theory are investigated. It is shown in the nonrotating scale-invariant limit that the collision integral in the kinetic equation diverges for almost all spectral power-law exponents. These divergences come from resonant interactions with the smallest horizontal wavenumbers and/or the largest horizontal wavenumbers with extreme scale separations. A small domain is identified in which the scale-invariant collision integral converges and numerically find a convergent power-law solution. This numerical solution is close to the Garrett–Munk spectrum. Power-law exponents that potentially permit a balance between the infrared and ultraviolet divergences are investigated. The balanced exponents are generalizations of an exact solution of the scale-invariant kinetic equation, the Pelinovsky–Raevsky spectrum. A small but finite Coriolis parameter representing the effects of rotation is introduced into the kinetic equation to determine solutions over the divergent part of the domain using rigorous asymptotic arguments. This gives rise to the induced diffusion regime. The derivation of the kinetic equation is based on an assumption of weak nonlinearity. Dominance of the nonlocal interactions puts the self-consistency of the kinetic equation at risk. However, these weakly nonlinear stationary states are consistent with much of the observational evidence.
    Description
    Author Posting. © American Meteorological Society, 2010. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 40 (2010): 2605–2623, doi:10.1175/2010JPO4132.1.
    Collections
    • Physical Oceanography (PO)
    Suggested Citation
    Journal of Physical Oceanography 40 (2010): 2605–2623
     

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