  We investigate the effects of a nearby free surface on the stability of a
flexible plate in axial flow. Confinement by rigid boundaries is known to
affect flag flutter thresholds and fluttering dynamics significantly, and this
work considers the effects of a more general confinement involving a deformable
free surface. To this end, a local linear stability is proposed for a flag in
axial uniform flow and parallel to a free surface, using one-dimensional beam
and potential flow models to revisit this classical fluid-structure interaction
problem. The physical behaviour of the confining free surface is characterized
by the Froude number, corresponding to the ratio of the incoming flow velocity
to that of the gravity waves. After presenting the simplified limit of infinite
span (i.e. two-dimensional problem), the results are generalized to include
finite-span and lateral confinement effects. In both cases, three unstable
regimes are identified for varying Froude number. Rigidly-confined flutter is
observed for low Froude number, i.e. when the free surface behaves as a rigid
wall, and is equivalent to the classical problem of the confined flag. When the
flow and wave velocities are comparable, a new instability is observed before
the onset of flutter (i.e. at lower reduced flow speed) and results from the
resonance of a structural bending wave and one of the fundamental modes of
surface gravity waves. Finally, for large Froude number (low effect of
gravity), flutter is observed with significant but passive deformation of the
free surface in response of the flag's displacement.
