“…To characterize the critical states of the flow, we use the Landau equation, which describes the evolution of the flow perturbation in its weakly nonlinear regime, and it can be determined as (Landau & Lifshitz 1976; Guckenheimer & Holmes 1983; Kang et al. 2017, 2019 a , b ) Here, is the linear growth rate of the perturbation and l is the Landau constant, where the sign of l indicates the nature of the bifurcation (i.e. supercritical versus subcritical).…”