  We investigate the dynamics and energy production capability of a flexible
piezoelectric plate submerged close to the free surface and exposed to incident
head gravity waves and current. A theoretical model is derived in which the
flag and its wake are represented with a vortex line while the body of the
fluid is considered to be inviscid. The model is employed to describe the
hydrodynamic interactions between a flexible plate, its wake, gravity incident
waves and the current. The model reveals two distinct vibration states of a
piezoelectric device corresponding to almost similar optimal energy production
levels. The first is associated with the cantilever fluttering mode of the
plate with limited dependency on the plate's flexibility across different
Froude numbers and incoming wave frequencies. The other resembles the
flow-induced flapping mode in more flexible plates, with the energy output
showing a higher dependency on plate flexibility. The concurrent existence of
these two energetic modes allows adjustment of the plate length to consistently
achieve the maximum energy production level across different flow conditions.
The role of the Froude number of the system's responses is explored and
correlated to the appearance of gravity wave groups on the surface, each
propagating with a different wavenumber. It is shown that a submergence depth
of less than half of the body length is required to reach a high energetic
condition in subcritical and critical flows. Finally, the optimal inductive and
resistive values are related to proper matching between flow, mechanical and
electrical timescales.
