A Proof for the Equivalence of Two Upper Bounds for the Growth of Disturbances from Barotropic Instability

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Abstract

A previous study proposed two methods for calculating the upper bound of the growth of disturbances from barotropic instability of a zonal flow in a two-dimensional incompressible fluid on a rotating sphere. The study conjectured that these two upper bounds are equivalent. One method was based on the conservation of the domain-averaged pseudomomentum density, and the other solved a minimization problem under the constraints of the conservations of all Casimir invariants and the total absolute angular momentum. In this study, this conjecture is verified, i.e., a proof is presented for their equivalence by developing an annealing-like procedure to reach the absolute vorticity profile that corresponds to the upper bound. The procedure also provides a more efficient method to calculate the upper bound.

Journal

  • Journal of the Meteorological Society of Japan. Ser. II

    Journal of the Meteorological Society of Japan. Ser. II 91(6), 843-850, 2013

    Meteorological Society of Japan

Codes

  • NII Article ID (NAID)
    120005539355
  • NII NACSIS-CAT ID (NCID)
    AA00702524
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    0026-1165
  • Data Source
    IR 
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