Barotropic and Baroclinic Instabilities
Part of the
International Centre for Mechanical Sciences
book series (CISM, volume 329)
The stability of a given flow field is a central question in the consideration of the realisability and persistence of a flow. This question is most simply addressed by considering the linear stability of the flow. A small perturbation is made to the given flow field and the tendency for this perturbation to grow, or decay is determined. Since the perturbation is small the equations of motion are linearised about this basic state, and these linearised equations often yield mode-like solutions with time-dependence of the form e iτt, where t is time and σ the frequency of the mode. If Im(σ) < 0, the mode grows exponentially and the flow is said to be linearly unstable.
KeywordsRossby Wave Froude Number Potential Vorticity Baroclinic Instability Isopycnal Surface
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Drazin, P.G. & Reid, W.H. 1991 Hydrodynamic stability C.U. P
Kuo H.L. 1949. Dynamic instability of two-dimensional non-divergent flow in a barotropic atmosphere. J. Meteorology
, 105–122.CrossRefGoogle Scholar
Eady, E.T. 1949. Long waves and cyclone waves. Tellus
, 33–52.CrossRefMathSciNetGoogle Scholar
Killworth, P.D. 1980. Barotropic and baroclinic instability in rotating stratified fluids. Dynamics of Atmospheres and Oceans
, 143–184.ADSCrossRefGoogle Scholar
Ripa, P. 1983. General stability conditions for zonal flows in a one-layer model on the beta-plane of the sphere. J. Fluid Mech.
, 436–489.CrossRefMathSciNetGoogle Scholar
Hayashi, Y. & Young, W.R. 1987. Stable and unstable shear modes on rotating parallelflows in shallow water. J. Fluid Mech.
, 477–504.ADSCrossRefMATHGoogle Scholar
Sakai, S. 1989. Rossby-Kelvin instability: a new type of ageostrophic instability caused by a resonance between Rossby waves and gravity waves. J. Fluid Mech.
, 149–176.ADSCrossRefMATHMathSciNetGoogle Scholar
Phillips, N.A. 1954. Energy transformations and meridional circulations associated with simple baroclinic waves in a two-level, quasigeostrophic model. Tellus
, 273–286.ADSCrossRefGoogle Scholar
Pedlosky, J., 1979. Geophysical Fluid Dynamics (Springer-Verlag).
© Springer-Verlag Wien 1992