2015/02/11 by Henk A. Dijkstra, Taylan Şengül, Dijkstra, Henk +5
Computer Science · Engineering · Environmental Science · #Atmospheric and Oceanic Physics (physics.ao-ph) #Climate variability and models #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.1502.04974
openalex publication_date 2015/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The main aim of this paper is to describe the dynamic transitions in flows described by the two-dimensional, barotropic vorticity equation in a periodic zonal channel. In \citeCGSW03, the existence of a Hopf bifurcation in this model as the Reynolds number crosses a critical value was proven. In this paper, we extend the results in \citeCGSW03 by addressing the stability problem of the bifurcated periodic solutions. Our main result is the explicit expression of a non-dimensional number γ which controls the transition behavior. We prove that depending on γ, the modeled flow exhibits either a continuous (Type I) or catastrophic (Type II) transition. Numerical evaluation of γ for a physically realistic region of parameter space suggest that a catastrophic transition is preferred in this flow.