  We experimentally study gravity-capillary wave turbulence on the interface
between two immiscible fluids of close density with free upper surface. We
locally measure the wave height at the interface between both fluids by means
of a highly sensitive laser Doppler vibrometer. We show that the inertial range
of the capillary wave turbulence regime is significantly extended when the
upper fluid depth is increased: The crossover frequency between the gravity and
capillary wave turbulence regimes is found to decrease whereas the dissipative
cut-off frequency of the spectrum is found to increase. We explain these
observations by the progressive decoupling between waves propagating at the
interface and the ones at the free surface, using the full dispersion relation
of gravity-capillary waves in a two-layer fluid of finite depths. The cut-off
evolution is due to the disappearance of parasitic capillaries responsible for
the main wave dissipation for a single fluid.
