  We demonstrate the existence of interface-induced turbulence, an emergent
nonequilibrium statistically steady state (NESS) with spatiotemporal chaos,
which is induced by interfacial fluctuations in low-Reynolds-number
binary-fluid mixtures. We uncover the properties of this NESS via direct
numerical simulations (DNSs) of cellular flows in the
Cahn-Hilliard-Navier-Stokes (CHNS) equations for binary fluids. We show that,
in this NESS, the shell-averaged energy spectrum $E(k)$ is spread over several
decades in the wavenumber $k$ and it exhibits a power-law region, indicative of
turbulence but without a conventional inertial cascade. To characterize the
statistical properties of this turbulence, we compute, in addition to $E(k)$,
the time series $e(t)$ of the kinetic energy and its power spectrum,
scale-by-scale energy transfer as a function of $k$, and the energy dissipation
resulting from interfacial stresses. Furthermore, we analyze the mixing
properties of this low-Reynolds-number turbulence via the mean-square
displacement (MSD) of Lagrangian tracer particles, for which we demonstrate
diffusive behavior at long times, a hallmark of strong mixing in turbulent
flows.
