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Volume 19 Issue 6

Nov.  2002

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Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 2002 >  19(6): 1079-1090

Nonlinear Saturation of Baroclinic Instability in the Phillips Model: The Case of Energy

  • 1.

    Key Laboratoryfor Mesoscale Severe Weather of Ministy of Education LMSWE/ MOE,Department o f Atrnospheric Sciences, Nanfing University, Nanfing 210093;Institute of Meteorology, PLA University of Science and Technology, Nanjing 211101,Institute of Meteorology, PLA University of Science and Technology, Nanjing 211101


doi: 10.1007/s00376-002-0066-0

  • A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model-the case of energy-is studied within the context of Arnold's second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd's; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances φ'i at any time.
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    • Manuscript History

    Manuscript received: 10 November 2002
    Manuscript revised: 10 November 2002
    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

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    Nonlinear Saturation of Baroclinic Instability in the Phillips Model: The Case of Energy

    • 1. Key Laboratoryfor Mesoscale Severe Weather of Ministy of Education LMSWE/ MOE,Department o f Atrnospheric Sciences, Nanfing University, Nanfing 210093;Institute of Meteorology, PLA University of Science and Technology, Nanjing 211101,Institute of Meteorology, PLA University of Science and Technology, Nanjing 211101
    • Manuscript received: 2002-11-10
    • Manuscript revised: 2002-11-10

    Abstract: A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model-the case of energy-is studied within the context of Arnold's second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd's; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances φ'i at any time.

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