An Enstrophy-Based Analysis of the Turbulence-Interface Interactions Across the Scales

This study presents an analysis of the turbulence-interface interactions during the sheet fragmentation process based on the concept of enstrophy transport across the length scales. We carried out fully-resolved volume of fluid (VOF) simulations of homogeneous isotropic turbulence (HIT) in the presence of an initially flat sheet of interface and analyzed the spectral rates of enstrophy production/destruction due to different mechanisms in the enstrophy transport equation. We highlight the scale-dependent nature of the surface tension mechanism that interacts with the vortex stretching term and shapes the evolution of interfacial turbulence.  It is demonstrated that the spectral rate of surface tension term in enstrophy transport equation changes sign at a characteristic length scale distinguishing between the nature of interfacial events: negative for enstrophy-reducing fragmentation and positive for enstrophy-releasing surface minimization and coalescence. We further show that at another characteristic length scale, the rate of enstrophy production by the surface tension balances the disruptive mechanism of vortex stretching. This corresponds to a similar length scale that the energy cascade of two-phase turbulence deviates from its single-phase similitude, and is also similar to the length scale at which the wavenumber spectrum of the volume fraction field starts to decay. The analysis further discloses that increasing sheet Weber number by lowering the surface tension coefficient, increasing density, and decreasing the viscosity of the sheet all enhance the vortex stretching effect across the scales and dilate the spectral range at which the surface tension contribution is negative toward the smaller scales, and thus facilitate the fragmentation. Whereas the higher surface tension coefficient, higher viscosity, and lower density ratio expand the spectral range associated with a positive contribution of surface tension toward the larger scales and suppress fragmentation events. This enstrophy-based description offers a new interpretation of the range of maximum stable droplets in turbulence. Accordingly, an improved approximation for the Hinze scale is proposed and tested which could serve as a useful implication of the findings for the DNS and LES of two-phase flows.