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We study two-dimensional (2D) binary-fluid turbulence by carrying out anextensive direct numerical simulation (DNS) of the forced, statistically steadyturbulence in the coupled Cahn-Hilliard and Navier-Stokes equations. In theabsence of any coupling, we choose parameters that lead (a) to spinodaldecomposition and domain growth, which is characterized by the spatiotemporalevolution of the Cahn-Hilliard order parameter $\phi$, and (b) the formation ofan inverse-energy-cascade regime in the energy spectrum $E(k)$, in which energycascades towards wave numbers $k$ that are smaller than the energy-injectionscale $k_{inj}$ in the turbulent fluid. We show that theCahn-Hilliard-Navier-Stokes coupling leads to an arrest of phase separation ata length scale $L_c$, which we evaluate from $S(k)$, the spectrum of thefluctuations of $\phi$. We demonstrate that (a) $L_c \sim L_H$, the Hinze scalethat follows from balancing inertial and interfacial-tension forces, and (b)$L_c$ is independent, within error bars, of the diffusivity $D$. We elucidatehow this coupling modifies $E(k)$ by blocking the inverse energy cascade at awavenumber $k_c$, which we show is $\simeq 2\pi/L_c$. We compare our work withearlier studies of this problem.

Two-dimensional Turbulence in Symmetric Binary-Fluid Mixtures: Coarsening Arrest by the Inverse Cascade