We use pseudo-spectral Direct Numerical Simulation (DNS), coupled with a Phase Field Method (PFM), to investigate the turbulent flow of two immiscible liquid layers inside a channel. This setting, in which the two fluids have the same density but different viscosity (so to mimick the flow of oil and water), allows for the interplay between inertial, viscous and surface tension forces to be studied in the absence of gravity. We focus on the interaction between capillary waves and turbulence at the liquid-liquid interface. Spatiotemporal spectral analysis of the capillary wave field shows wave propagation that is in agreement with the theoretical dispersion relation. The one-dimensional wavenumber spectrum suggests an energy equipartition regime at larger wave scales and a transition to a sharp decay of wave energy at smaller scales taking place near the Kolmogorov-Hinze critical scale, where surface tension forces and turbulent inertial forces are balanced.
