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

• Published in: arXiv.org 2015-06
• Main Authors: Prasad Perlekar, Pal, Nairita, Pandit, Rahul
• Format: Article
• Language: English
• Subjects: Cascades; Coarsening; Computational fluid dynamics; Computer simulation; Coupling; Direct numerical simulation; Domain names; Energy spectra; Fluid flow; Navier-Stokes equations; Order parameters; Phase separation; Spinodal decomposition; Turbulence; Variation; Wavelengths
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1506.08524

We study two-dimensional (2D) binary-fluid turbulence by carrying out an extensive direct numerical simulation (DNS) of the forced, statistically steady turbulence in the coupled Cahn-Hilliard and Navier-Stokes equations. In the absence of any coupling, we choose parameters that lead (a) to spinodal decomposition and domain growth, which is characterized by the spatiotemporal evolution of the Cahn-Hilliard order parameter \(\phi\), and (b) the formation of an inverse-energy-cascade regime in the energy spectrum \(E(k)\), in which energy cascades towards wave numbers \(k\) that are smaller than the energy-injection scale \(k_{inj}\) in the turbulent fluid. We show that the Cahn-Hilliard-Navier-Stokes coupling leads to an arrest of phase separation at a length scale \(L_c\), which we evaluate from \(S(k)\), the spectrum of the fluctuations of \(\phi\). We demonstrate that (a) \(L_c \sim L_H\), the Hinze scale that follows from balancing inertial and interfacial-tension forces, and (b) \(L_c\) is independent, within error bars, of the diffusivity \(D\). We elucidate how this coupling modifies \(E(k)\) by blocking the inverse energy cascade at a wavenumber \(k_c\), which we show is \(\simeq 2\pi/L_c\). We compare our work with earlier studies of this problem.