| Phillips模式的斜压不稳定的非线性饱和问题:能量情形 |
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| 作者姓名： | Xiang Jie Sun Litan |
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| 作者单位： | 项杰(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);孙立潭(Institute of Meteorology, PLA University of Science and Technology, Nanjing 211101)
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| 基金项目： | This project was supported jointly by the National Natural Science Foundation of China under Grant Nos. 49455007, 40075011, and 40075014, and the China Postdoctoral Science Foundation, |
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| 摘 要： | 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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| 关 键 词： | 能量 非线性饱和 斜压不稳定 Phillips模式 垂直速度切变 二阶修正 |
| 收稿时间： | 8 January 2002 |
Nonlinear saturation of baroclinic instability in the Phillips model: The case of energy |
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| Xiang Jie,Sun Litan.Nonlinear saturation of baroclinic instability in the Phillips model: The case of energy[J].Advances in Atmospheric Sciences,2002,19(6):1079-1090. |
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| Authors: | Jie Xiang Sun Litan |
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| Institution: | 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 |
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| 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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| Keywords: | nonlinear saturation baroclinic instability Phillips model |
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