2014/08/04 by Zhi‐Min Chen, Zhi-Min Chen, Chen, Zhi-Min
Earth and Planetary Sciences · Environmental Science · Mathematics · #35B32 #35B35 #35Q35 #76B03 #86A10 #Analysis of PDEs (math.AP) #Climate variability and models #FOS: Mathematics #Meteorological Phenomena and Simulations #Oceanographic and Atmospheric Processes #math.AP #msc:35B32 #msc:35B35 #msc:35Q35 #msc:76B03 #msc:86A10
paper · pdf · doi:10.48550/arxiv.1408.0708
20 pages, 0 figures, 30 references
openalex publication_date 2014/08/04 · arxiv created 2017/06/22 · arxiv updated 2017/06/23 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
The quasi-geostrophic equation or the Euler equation with dissipation studied in the present paper is a simplified form of the atmospheric circulation model introduced by Charney and DeVore [J. Atmos. Sci. 36(1979), 1205-1216] on the existence of multiple steady states to the understanding of the persistence of atmospheric blocking. The fluid motion defined by the equation is driven by a zonal thermal forcing and an Ekman friction forcing measured by κ>0. It is proved that the steady-state solution is unique for κ>1 while multiple steady-state solutions exist for κ<κcrit with respect to critical value κcrit<1. Without involvement of viscosity, the equation has strong nonlinearity as its nonlinear part contains the highest order derivative term. Steady-state bifurcation analysis is essentially based on the compactness, which can be simply obtained for semi-linear equations such as the Navier-Stokes equations but is not available for the quasi-geostrophic equation in the Euler formulation. Therefore the Lagrangian formulation of the equation is employed to gain the required compactness.