2017/04/17 by Ming Cai, Cai, Ming, Marcos Hernández +5
Earth and Planetary Sciences · Environmental Science · #Atmospheric and Oceanic Physics (physics.ao-ph) #Climate variability and models #FOS: Physical sciences #Oceanographic and Atmospheric Processes #Tropical and Extratropical Cyclones Research #baroclinic instability #continuous transition #dynamic transition theory #dynamic transitions #jump transition #two-layer quasigeostrophic channel flow
paper · pdf · doi:10.48550/arxiv.1705.07989
openalex publication_date 2017/04/17 · openalex created_date 2017/06/05 · openalex updated_date 2026/07/28
The main objective of this article is to derive a mathematical theory associated with the nonlinear stability and dynamic transitions of the basic shear flows associated with baroclinic instability, which plays a fundamental role in the dominant mechanism shaping the cyclones and anticyclones that dominate weather in mid-latitudes, as well as the mesoscale eddies that play various roles in oceanic dynamics and the transport of tracers. This article provides a general transition and stability theory for the two-layer quasi-geostrophic model originally derived by Pedlosky \citeped1970. We show that the instability and dynamic transition of the basic shear flow occur only when the Froude number F>(γ2+1)/2, where γ is the weave number of lowest zonal harmonic. In this case, we derive a precise critical shear velocity Uc and a dynamic transition number b, and we show that the dynamic transition and associated flo0w patterns are dictated by the sign of this transition number. In particular, we show that for b>0, the system undergoes a continuous transition, leading to spatiotemporal flow oscillatory patterns as the shear velocity U crosses Uc; for b<0, the system undergoes a jump transition, leading to drastic change and more complex transition patterns in the far field, and to unstable period solutions for U