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Volume 29 Issue 4

Jul.  2012

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Article >  ADVANCES IN ATMOSPHERIC SCIENCES  > 2012 >  29(4): 690-694

On the Generalized Ertel--Rossby Invariant

  • 1.

    Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081;Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190;Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, Graduate University of Chinese Academy of Sciences, Beijing 100040


doi: 10.1007/s00376-012-1145-5

  • A new invariant called the generalized Ertel--Rossby invariant (GER) was developed in this study. The new invariant is given by the dot product of the generalized vorticity and the generalized velocity. The generalized vorticity is the absolute vorticity minus the cross--product of the gradient of Lagrangian--time integrated temperature and the gradient of entropy. The generalized velocity is the absolute velocity minus the sum of the gradient of Lagrangian--time integrated kinetic potential and the Lagrangian--time integrated temperature multiplied by the gradient of entropy. In addition to the traditional potential vorticity, the GER invariant may provide another useful tool to study the atmospheric dynamic processes for weather phenomena ranging from large scales to small scales.
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    • Manuscript History

    Manuscript received: 10 July 2012
    Manuscript revised: 10 July 2012
    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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    On the Generalized Ertel--Rossby Invariant

    • 1. Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081;Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100190;Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, Graduate University of Chinese Academy of Sciences, Beijing 100040
    • Manuscript received: 2012-07-10
    • Manuscript revised: 2012-07-10

    Abstract: A new invariant called the generalized Ertel--Rossby invariant (GER) was developed in this study. The new invariant is given by the dot product of the generalized vorticity and the generalized velocity. The generalized vorticity is the absolute vorticity minus the cross--product of the gradient of Lagrangian--time integrated temperature and the gradient of entropy. The generalized velocity is the absolute velocity minus the sum of the gradient of Lagrangian--time integrated kinetic potential and the Lagrangian--time integrated temperature multiplied by the gradient of entropy. In addition to the traditional potential vorticity, the GER invariant may provide another useful tool to study the atmospheric dynamic processes for weather phenomena ranging from large scales to small scales.

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