Bifurcation properties of quasi-geostrophic, barotropic models and their relation to atmospheric blocking

E. Källen

doi:10.3402/tellusa.v34i3.10809

Bifurcation properties of quasi-geostrophic, barotropic models and their relation to atmospheric blocking

Tellus

Volume 34 (1982): Issue 3

By: E. Källen

Open Access

|Jan 1982

Abstract

The bifurcation properties of a low-order, barotropic model on the sphere with orographic and a Newtonian type of vorticity forcing are reviewed. The low-order model results that multiple equilibria develop as a result of a sufficiently strong, long-wave, orographic forcing and that a suitably positioned wave vorticity forcing can enhance this bifurcation mechanism are verified with a high resolution, spectral model. The high-resolution model is integrated in time to find stable steady states. Bifurcations into multiple equilibria appear as sudden jumps in the amplitudes of the model components when the forcing is slowly changing in time.

A limited diagnostic study of some blocking events in the Northern Hemisphere during the months January–March 1979 is also presented. Calculations of the mountain torque and the eddy activity in certain regions partly support the blocking mechanism originally proposed by Charney and DeVore, and further developed by Källen.

References

Bengtsson , L. , Kanamitsu , M. , Milberg , P. and Uppala , S . 1981 . The FGGE III-b system at ECMWF. To appear in Bull. Amer. Meteorol. Soc.
Search in Google Scholar Back to article
Charney , J . G. and DeVore, J. G. 1979. Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci. 36, 1205 – 1216.
Search in Google Scholar Back to article
Davey , M. K . 1980 . A quasi-linear theory for rotating flow over topography. Part I: Steady 11-plane channel . J. Fluid Mech . 99 , 267 – 292 .
Search in Google Scholar Back to article
Davey , M. K . 1981 . A quasi-linear theory for rotating flow over topography. Part II: Beta-plane annulus . J. Fluid Mech . 103 , 297 – 320 .
Search in Google Scholar Back to article
Hoskins , B. 1 1973. Stability of the Rossby-Haurwits wave. Q. J. R. Meteorol. Soc. 99, 723 – 745.
Search in Google Scholar Back to article
Hoskins , B. J. and Simmons , A. J . 1975 . A multi-layer spectral model and the semi-implicit method . Q. J. R. Meteorol. Soc . 101 , 637 – 655 .
Search in Google Scholar Back to article
Källén , E . 1981 . The non-linear effects of orographic and momentum forcing in a low-order, barotropic model . J. Atmos. Sc L 39 , 2150 – 2163 .
Search in Google Scholar Back to article
Marsden , J. E. and McCracken , M . 1976 . The Hopf bifurcation and its applications. New York: Springer Verlag, pp. 408.
Search in Google Scholar Back to article
McWilliams , J. C. 1980 . An application of equivalent modons to atmospheric blocking. Dyn. Atmos. Oceans 5, 43 - 66.
Search in Google Scholar Back to article
Saltzman , B . 1970 . Large-scale atmospheric energetics in wave number domain . Rev. Geophys. and Space Phys . 8 , 289 – 302 .
Search in Google Scholar Back to article
Savijärvi , H . 1978 . The interaction of the monthly mean flow and large scale transient eddies in two different circulation types, Part II . Geophysica 14 , 207 – 229 .
Search in Google Scholar Back to article
Steinberg , H. L. , Wiin-Nielsen , A. and Yang , C.-H . 1971 . On non-linear cascades in large-scale atmospheric flow J . Geophys. Res. 76 , 8629 – 8640 .
Search in Google Scholar Back to article
Vickroy , J. G. and Dutton , J. A . 1979 . Bifurcation and catastrophe in a simple, forced, dissipative quasi-geostrophic flow. J. Atmos. Sc i . 36 , 42 – 52 .
Search in Google Scholar Back to article
Webster , P. J . 1981 . Mechanisms determining the atmospheric response to sea surface temperature anomalies . J. Atmos, Sci . 38 , 554 – 571 .
Search in Google Scholar Back to article
Wiin-Nielsen , A. C . 1979 . Steady states and stability properties of a low-order barotropic system with forcing and dissipation . Tellus 31 , 375 – 386 .
Search in Google Scholar Back to article