Experiments with layers of salt and sugar solution separated by a diff
usive interface are described. Interfacial waves were spontaneously ge
nerated by the convection once the system evolved to a critical value
of the density-anomaly ratio R-rho = beta Delta S/alpha Delta T. The w
aves locally modulated the interfacial fluxes by modifying the interfa
ce thickness and thereby organized otherwise random convective motions
into large-scale circulations. In turn, the waves themselves persiste
d for unusually long times owing to energy input from the organized co
nvection. The dependence of the wave speed on the layer properties and
channel dimensions was successfully predicted by assuming that coupli
ng requires a matching of the wave and convection speeds, and that the
system selects waves of an amplitude for which this resonance can occ
ur. This 'wave-convection coupling' also appeared to increase the inte
rfacial fluxes at low R-rho. The interaction of waves and convection m
ay be important for oceanic thermohaline staircases and other systems
where convection is driven by interfacial fluxes.