Multiple Stable States of Quasi-geostrophic Barotropic Flow over Sinusoidal Topography

Abstract

A multi-variables model of quasi-geostrophic barotropic flow over sinusoidal topography is constructed to investigate the bifurcation properties of the nonlinear system and to assess the availability of the low-order models by Charney and DeVore (1979) and Yoden (1985) on the same problem.
When the horizontal diffusion by small-scale eddies is incorporated into the model (the Reynolds number is 10³), multiplicity of stable steady solutions is obtained for a wide range of external parameters contrary to the cases of high Reynolds numbers (10⁴ and ∞) . Periodic solutions are also obtained which branch off a steady solution by the Hopf bifurcation.
These results support qualitatively some of those obtained in the low-order models, although some spurious properties due to the severe truncation are also recognized. Multiple flow equilibria first pointed out by Charney and DeVore (1979) could be demonstrated by laboratory experiments of rotating fluids.