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Original Research Papers

Linear amplification of marginally neutral baroclinic waves

Authors:

Hylke De Vries ,

University of Reading, Department of Meteorology, PO BOX 243, Earley Gate, Reading. RG6 6BB, GB
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Martin Ehrendorfer

University of Reading, Department of Meteorology, PO BOX 243, Earley Gate, Reading. RG6 6BB, GB
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Abstract

Baroclinic wave development is investigated for unstable parallel shear flows in the limit of vanishing normal-mode growth rate. This development is described in terms of the propagation and interaction mechanisms of two coherent structures, called counter-propagating Rossby waves (CRWs). It is shown that, in this limit of vanishing normal-mode growth rate, arbitrary initial conditions produce sustained linear amplification of the marginally neutral normal mode (mNM). This linear excitation of the mNM is subsequently interpreted in terms of a resonance phenomenon. Moreover, while the mathematical character of the normal-mode problem changes abruptly as the bifurcation point in the dispersion diagram is encountered and crossed, it is shown that from an initial-value (CRW) viewpoint, this transition is smooth. Consequently, the resonance interpretation remains relevant (albeit for a finite time) for wavenumbers slightly different from the ones defining cut-off points. The results are further applied to a two-layer version of the classic Eady model in which the upper rigid lid has been replaced by a simple stratosphere.

How to Cite: De Vries, H. and Ehrendorfer, M., 2008. Linear amplification of marginally neutral baroclinic waves. Tellus A: Dynamic Meteorology and Oceanography, 60(5), pp.1079–1088. DOI: http://doi.org/10.1111/j.1600-0870.2008.00355.x
  Published on 01 Jan 2008
 Accepted on 27 Jun 2008            Submitted on 31 Jan 2008

References

  1. Boyce , W. and DiPrima , R. 2003 . Elementary Differential Equations and Boundary Value Problems 7th Edition . John Wiley and Sons , Inc. USA .  

  2. Bretherton , F. P. 1966 . Critical layer instability in baroclinic flows . Quart. J. Roy. Meteor. Soc . 92 , 325 – 334 .  

  3. Chang , E. K. M. 1992 . Resonating neutral modes of the Eady model. J. Atmos. Sci. 49 , 2452-2463. Baroclinic instability , Cyclogenesis , Neutral .  

  4. Charney , J. G. 1947 . The dynamics of long waves in a baroclinic westerly current . J. Atmos. Sci . 4 , 135 – 162 .  

  5. Charney , J. G. and Stern , M. E. 1962 . On the stability of internal baro-clinic jets in a rotating atmosphere . J. Atmos. Sci . 19 , 159 – 172 .  

  6. Davies , H. C. and Bishop , C. H. 1994 . Eady edge waves and rapid development . J. Atmos. Sci . 51 , 1930 – 1946 .  

  7. De Vries , H. and Opsteegh , J. D. 2005 . Optimal perturbations in the Eady model: resonance versus PV unshielding . J. Atmos. Sci . 62 ( 2 ), 492 – 505 .  

  8. De Vries , H. and Opsteegh , J. D. 2007 . Interpretation of discrete and continuum modes in a two-layer Eady model . Tellus 59A , 182 – 197 .  

  9. Dirren , S. and Davies , H. C. 2004 . Combined dynamics of boundary and interior perturbations in the Eady setting . J. Atmos. Sci . 61 , 1549 – 1565 .  

  10. Eady , E. T. 1949 . Long waves and cyclone waves . Tellus 1 , 33 – 52 .  

  11. Fjørtoft , R. 1951 . Stability properties of large-scale atmospheric disturbances. In: Compendium of Meteorology . American Meteorological Society, Boston , USA .  

  12. Green , J. S. A. 1960 . A problem in baroclinic stability . Quart. J. Roy. Meteor Soc . 86 , 237 – 251 .  

  13. Heifetz , E. and Methven , J. 2005 . Relating optimal growth to coun-terpropagating Rossby waves in shear instability . Physics of Fluids 17 ( 1 ), 1 – 14 .  

  14. Heifetz , E. , Bishop , C. H. , Hoskins , B. J. and Methven , J. 2004a . The counter-propagating Rossby-wave perspective on baroclinic instabil-ity, I: mathematical basis . Quart. J. Roy. Meteor. Soc . 130 , 211 – 231 .  

  15. Heifetz , E. , Methven , J. , Hoskins , B. J. and Bishop , C. H. 2004b . The counter-propagating Rossby-wave perspective on baroclinic instabil-ity, II: application to the Charney model . Quart. J. Roy. Meteor Soc . 130 , 233 - 258 .  

  16. Hoskins , B. J. , McIntyre , M. E. and Robertson , A. W. 1985 . On the use and significance of isentropic potential voracity maps. Quart. J. Roy. Meteor Soc . 111 , 877 - 946 .  

  17. Jenkner , J. and Ehrendorfer , M. 2006 . Resonant continuum modes in the Eady model with rigid lid . J. Atmos. Sci . 63 ( 2 ), 765 – 773 .  

  18. Methven , J. , Heifetz , E. , Hoskins , B. J. and Bishop , C. H. 2005 . The counter-propagating Rossby-wave perspective on baroclinic instabil-ity, DI: primitive-equation disturbances on the sphere. Quart. J. Roy. Meteor Soc . 131 , 1393 - 1424 .  

  19. Müller , J. C. 1991 . Baroclinic instability in a two-layer, vertically semi-infinite domain. Tellus 43A , 275 - 284 .  

  20. Pedlosky , J. 1987 . Geophysical Fluid Dynamics 2nd Edition . Prentice Hall , NJ .  

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