  We conduct direct numerical simulation (DNS) of the
Cahn-Hilliard-Navier-Stokes (CHNS) equations to investigate the statistical
properties of the turbulent phase-separating symmetric binary-fluid mixture.
Turbulence causes an arrest of the phase-separation which leads to the
formation of a statistically steady emulsion. We characterize turbulent
velocity fluctuations in an emulsion for different values of the Reynolds
number and the Weber number. Our scale-by-scale kinetic energy budget analysis
shows that the interfacial terms in the CHNS provide an alternate route for the
kinetic energy transfer. By studying the probability distribution function
(PDF) of the energy dissipation rate, the vorticity magnitude, and the
joint-PDF of the velocity-gradient invariants we show that the statistics of
the turbulent fluctuations do not change with the Weber number.
