Stability diagram obtained by solving the eigenvalue problem **16**, **2** parametrized in terms of the scaled added mass, ρ, and the scaled flow velocity, *u*_{0}. The thin dashed line represents the transition curve using the quasi-steady approximation where *C* = 1; for values of ρ, *u*_{0} below this line, the flag is stable, and for values above it, it is unstable. The thin solid line represents the transition curve when vortex shedding is taken into account, i.e., *C* ≠ 1. The role of the third dimension and flag tension is considered in the appendices and changes the marginal stability curve slightly. The bold solid line is obtained by including three-dimensional effects using a simple model (see *Appendix 1*) for a flag of aspect ratio *r* = 2.5, and the bold dashed solid line takes into account the tension in the flag that arises due to viscous effects via a simple estimate of the Blasius boundary layer (see *Appendix 2*) with *Re* = 10^{4}. The dots correspond to experimental data characterizing the transition to flutter in three-dimensional flows past flexible sheets of paper (); the large error bars are a consequence of the variations due to three-dimensional effects as well as regions of bistability where both the flapping and stationary state are stable. (*Inset*) The dimensionless wavenumber of the instability *q* = (ω/2*u*_{0}) as a function of ρ. When ρ ≪ 1, *q* tends to be zero and *C*(*q*) → 1.

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