Theories of Multiple Equilibria-A Critical Reexamination. Part I: Barotropic Models

View More View Less
  • 1 Mathematics Department, Massachusetts Institute of Technology, Cambridge, MA 02139
© Get Permissions
Restricted access

Abstract

Previous results claiming the existence of multiple equilibria based on simple barotropic or two-layer models of the atmosphere are reexamined. While not ruling out the existence of multiple equilibria we find that the application of these results to the atmosphere, especially with regard to high/low zonal index and zonal/blocked situations, is probably problematic. Results based on truncated low-order models are found to change drastically when full nonlinearity is retained. Although multiple equilibria may still exist in some nonlinear models in some restricted parameter regimes, it is argued that the parameter values adopted in previous studies are probably not physically based.

Mathematically interesting properties of the nonlinear system, such as resonance bending, hysteresis, bifurcation and multiplicity of solutions are also discussed.

Abstract

Previous results claiming the existence of multiple equilibria based on simple barotropic or two-layer models of the atmosphere are reexamined. While not ruling out the existence of multiple equilibria we find that the application of these results to the atmosphere, especially with regard to high/low zonal index and zonal/blocked situations, is probably problematic. Results based on truncated low-order models are found to change drastically when full nonlinearity is retained. Although multiple equilibria may still exist in some nonlinear models in some restricted parameter regimes, it is argued that the parameter values adopted in previous studies are probably not physically based.

Mathematically interesting properties of the nonlinear system, such as resonance bending, hysteresis, bifurcation and multiplicity of solutions are also discussed.

Save