Figure 1

Computed stability boundary in the $R_1{R}_2$ plane. The upper solid boundary gives the smallest $R_2$ above which a small leading-edge forcing ($y(t)={10}^{-5}(2t{)}^2{e}^{-(2t{)}^2}$) does not lead to flapping. The lower solid boundary is the largest $R_2$ below which such forcing leads to exponential growth of elastic energy in time until the flag saturates with $O(1)$ flapping, as shown in Figs. 1 and 2 of 1. The solid line gives the scaling $R_1\sim R_2$ for comparison at small flag masses. The black crosses mark the cases shown in Fig. 2 of 1 [upper cross is (a) and (b), and lower is (c)]. The dashed line shows the stability boundary from the reduced model of 2, and the dash-dotted line the corresponding boundary plotted in Fig. 3 of the reduced model of 3 (showing only the portion $R_2\approx \mathrm{const}$, but having the same asymptotic scalings as the model here and in 2). The dotted line (with cusps) is the stability boundary for the 2D model of 4.Reuse & Permissions