Fig. 5.

Stability diagram of the trivial solution in the $(\alpha ,H_0)$ parameter space. The solid lines mark the critical curves for equal inlet-pressure [Eqs. (30)–(39), blue] and fixed-flux [Eq. (41), red] boundary conditions. The black dashed line represents the asymptotic solution for $\alpha \ll 1$, while the black dash-dotted lines mark the asymptotes for $H_0$ when $\alpha \gg 1$. The blue crosses indicate the transcritical bifurcation points of the steady-state solutions ($H_T$) for fixed inlet-pressure conditions as discussed in Sect. 3.1 (Color figure online)