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Efficient Anomalous Forcings for Linear Problems


doi: 10.1007/BF02658164

  • For linear forcing problems, a method is developed to provide a set of forcing modes which form a complete orthonormal basis for the finite-time response to steady forcing in the energy inner product space. The forcing modes are found by calculating eigenvectors of a positive definite and symmetric matrix determined from given equations of motion. The amplitude of responses to forcing modes is given in terms of the associated eigenvalues. This method is used in a nondivergent barotropic model linearized about the 300 hPa zonally-varying climatological flow both for northern summertime and wintertime. The results show that the amplitude of response varies considerably with dif-ferent forcing modes. Only a few of forcing modes associated with the leading eigenvalues, called efficient forcing mode, can excite significant response. The efficient forcing modes possess highly localized spatial structure with wavetrain appearance. Most of the efficient forcings are located to the south of regions of the jet cores. The forcings located over polar regions are also efficient. In addition, the response is larger in wintertime than in summertime for a given forcing.
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Manuscript History

Manuscript received: 10 October 1994
Manuscript revised: 10 October 1994
通讯作者: 陈斌, bchen63@163.com
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    沈阳化工大学材料科学与工程学院 沈阳 110142

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Efficient Anomalous Forcings for Linear Problems

  • 1. Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100080,Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100080

Abstract: For linear forcing problems, a method is developed to provide a set of forcing modes which form a complete orthonormal basis for the finite-time response to steady forcing in the energy inner product space. The forcing modes are found by calculating eigenvectors of a positive definite and symmetric matrix determined from given equations of motion. The amplitude of responses to forcing modes is given in terms of the associated eigenvalues. This method is used in a nondivergent barotropic model linearized about the 300 hPa zonally-varying climatological flow both for northern summertime and wintertime. The results show that the amplitude of response varies considerably with dif-ferent forcing modes. Only a few of forcing modes associated with the leading eigenvalues, called efficient forcing mode, can excite significant response. The efficient forcing modes possess highly localized spatial structure with wavetrain appearance. Most of the efficient forcings are located to the south of regions of the jet cores. The forcings located over polar regions are also efficient. In addition, the response is larger in wintertime than in summertime for a given forcing.

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