Baroclinic Instability in the Generalized Phillips’ Model Part II: Three-layer Model

Li Yang

doi:10.1007/s00376-000-0033-6

Impact Factor: 5.8

Volume 17 Issue 3

Sep. 2000

Article Contents

Article > ADVANCES IN ATMOSPHERIC SCIENCES > 2000 > 17(3): 413-432

Baroclinic Instability in the Generalized Phillips’ Model Part II: Three-layer Model

Li Yang

1.
LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029

Li Yang

doi: 10.1007/s00376-000-0033-6

Abstract
References
Related papers
PDF

Abstract:
The nonlinear stability of the three-layer generalized Phillips model, for which the velocity in each layer is constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol’d’s variational principle and a prior estimate method. The nonlinear stability criteria are established. For com-parison, the linear instability criteria are also obtained by using normal mode method, and the influences of the free parameter, β parameter and curvature in vertical profile of the horizontal velocity on the linear in-stability are discussed by use of the growth rate curves.The comparison between the nonlinear stability criterion and the linear one is made. It is shown that in some cases the two criteria are exactly the same in form, but in other cases, they are different. This phenom-enon, which reveals the nonlinear property of the linear instability features, is explained by the explosive resonant interaction (ERI). When there exists the ERI, i.e., the nonlinear mechanisms play a leading role in the dynamical system, the nonlinear stability criterion is different from the linear one; on the other hand, when there does not exist the ERI, the nonlinear stability criterion is the same as the linear one in form.
- The generalized Phillips’ model. Linear instability,
- Nonlinear stability
References

[1]	Liu Yongming, Mu Mu, 1994: Arnol’d’s Second Nonlinear Stability Theorem for General Multilayer Quasi-geostrophic Model, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 36-42. doi: 10.1007/BF02656991
[2]	Mu Mu, Wu Yonghui, Tang Mozhi, Liu Haiyan, 1999: Nonlinear Stability Analysis of the Zonal Flows at Middle and High Latitudes, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 569-580. doi: 10.1007/s00376-999-0032-1
[3]	Li Yang, Mu Mu, Wu Yonghui, 2000: A Study on the Nonlinear Stability of Fronts in the Ocean on a Sloping Continental Shelf, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 275-284. doi: 10.1007/s00376-000-0009-6
[4]	LIU Yongming, CAI Jingjing, 2006: On Nonlinear Stability Theorems of 3D Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 809-814. doi: 10.1007/s00376-006-0809-4
[5]	Li Yang, Mu Mu, 1996: On the Nonlinear Stability of Three-Dimensional Quasigeostrophic Motions in Spherical Geometry, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 203-216. doi: 10.1007/BF02656863
[6]	Liu Yongming, 1999: Nonlinear Stability of Zonally Symmetric Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 16, 107-118. doi: 10.1007/s00376-999-0007-2
[7]	Mu Mu, Guo Huan, Wang Jiafeng, LiYong, 2000: The Impact of Nonlinear Stability and Instability on the Validity of the Tangent Linear Model, ADVANCES IN ATMOSPHERIC SCIENCES, 17, 375-390. doi: 10.1007/s00376-000-0030-9
[8]	Xiang Jie, Sun Litan, 2002: Nonlinear Saturation of Baroclinic Instability in the Phillips Model: The Case of Energy, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 1079-1090. doi: 10.1007/s00376-002-0066-0
[9]	LU Weisong, SHAO Haiyan, 2003: Generalized Nonlinear Subcritical Symmetric Instability, ADVANCES IN ATMOSPHERIC SCIENCES, 20, 623-630. doi: 10.1007/BF02915505
[10]	Li Yang, Mu Mu, 1996: Baroclinic Instability in the Generalized Phillips’ Model Part I: Two-layer Model, ADVANCES IN ATMOSPHERIC SCIENCES, 13, 33-42. doi: 10.1007/BF02657026
[11]	He Jianzhong, 1994: Nonlinear Ultra-Long Wave and Its Stability, ADVANCES IN ATMOSPHERIC SCIENCES, 11, 91-100. doi: 10.1007/BF02656998
[12]	Lin Wantao, Ji Zhongzhen, Wang Bin, 2001: Computational Stability of the Explicit Difference Schemes of the Forced Dissipative Nonlinear Evolution Equations, ADVANCES IN ATMOSPHERIC SCIENCES, 18, 413-417. doi: 10.1007/BF02919320
[13]	JIANG Zhina, 2006: Applications of Conditional Nonlinear Optimal Perturbation to the Study of the Stability and Sensitivity of the Jovian Atmosphere, ADVANCES IN ATMOSPHERIC SCIENCES, 23, 775-783. doi: 10.1007/s00376-006-0775-x
[14]	Mu Mu, Zeng Qingcun, 1991: Criteria for the Nonlinear Stability of Three-Dimensional Quasi-Geostrophic Motions, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 1-10. doi: 10.1007/BF02657360
[15]	Lin Wantao, Ji Zhongzhen, Wang Bin, 2002: A Comparative Analysis of Computational Stability for Linear and Non-Linear Evolution Equations, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 699-704. doi: 10.1007/s00376-002-0009-9
[16]	Ren Shuzhan, 1991: Nonlinear Stability of Plane Rotating Shear Flow under Three-Dimensional Nondivergence Disturbances, ADVANCES IN ATMOSPHERIC SCIENCES, 8, 129-136. doi: 10.1007/BF02658089
[17]	Liu Yongming, Mu Mu, 1992: A Problem Related to Nonlinear Stability Criteria for Multi-layer Quasi-geostrophic Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 337-345. doi: 10.1007/BF02656943
[18]	Yong. L. McHall, 1992: Nonlinear Planetary Wave Instability and Blocking, ADVANCES IN ATMOSPHERIC SCIENCES, 9, 173-190. doi: 10.1007/BF02657508
[19]	Liu Shida, Liu Shikuo, 1985: NONLINEAR WAVES IN BAROTROPIC MODEL, ADVANCES IN ATMOSPHERIC SCIENCES, 2, 147-157. doi: 10.1007/BF03179747
[20]	Shen Xinyong, Ni Yunqi, Ding Yihui, 2002: On Problem of Nonlinear Symmetric Instability in Zonal Shear Flow, ADVANCES IN ATMOSPHERIC SCIENCES, 19, 350-364. doi: 10.1007/s00376-002-0027-7

PDF

Get Citation+

Export:

Article Metrics

Article Views: 1521 Times

PDF downloads: 1246 Times

Cited by: Times

Proportional views

Manuscript History

Manuscript received: 10 September 2000

Manuscript revised: 10 September 2000

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

Baroclinic Instability in the Generalized Phillips’ Model Part II: Three-layer Model

Li Yang

1. LASG, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029

Manuscript received: 2000-09-10
Manuscript revised: 2000-09-10

Abstract: The nonlinear stability of the three-layer generalized Phillips model, for which the velocity in each layer is constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol’d’s variational principle and a prior estimate method. The nonlinear stability criteria are established. For com-parison, the linear instability criteria are also obtained by using normal mode method, and the influences of the free parameter, β parameter and curvature in vertical profile of the horizontal velocity on the linear in-stability are discussed by use of the growth rate curves.The comparison between the nonlinear stability criterion and the linear one is made. It is shown that in some cases the two criteria are exactly the same in form, but in other cases, they are different. This phenom-enon, which reveals the nonlinear property of the linear instability features, is explained by the explosive resonant interaction (ERI). When there exists the ERI, i.e., the nonlinear mechanisms play a leading role in the dynamical system, the nonlinear stability criterion is different from the linear one; on the other hand, when there does not exist the ERI, the nonlinear stability criterion is the same as the linear one in form.

Keywords: