Multifractal Droplet Dynamics in Two-Dimensional, binary-fluid turbulence

etc15 Tracking Number 205

We present the most extensive direct numerical simulations, attempted so far, of statistically steady, homogeneous, isotropic turbulence in two-dimensional, binary-fluid mixtures with air-drag-induced friction. We model this mixture by using the Cahn-Hilliard-Navier-Stokes equations and choose parameters, e.g., the surface tension, such that we have a droplet of the minority phase moving inside a turbulent background of the majority phase. Our study reveals that a single droplet, whose mean radius lies in the inertial range of scales, (a) enhances the the forward-cascade part of the energy spectrum of two-dimensional turbulence and (b) stretches the tails of the PDF of the Okubo-Weiss parameter $\Lambda$. We show that the dynamics of the droplet is affected significantly by the turbulence in the fluid. In particular, the PDFs of the components of the acceleration shows wide, non-Guassian tails. We characterize the time dependence of the deformation of the droplet and show that it exhibits multifractality.