How the ramp-cliff structures in scalar turbulence vary with the Schmidt number and how to model that variation

In turbulent mixing of passive scalars, the ramp-cliff structures observed in one-dimensional cuts of the scalar field are responsible for a few important consequences, such as, departure from local isotropy, saturation of scaling exponents with respect to the moment-order. These results are established for the case of unity Schmidt number ($Sc$), given by the ratio of the kinematic viscosity of the fluid to the scalar diffusivity. In this talk, our first goal is to show how the above results vary with increasing $Sc$. We utilize a massive DNS database with the Taylor-scale Reynolds number in the range $140-650$, and Sc in the range $1-512$, for the case of passive scalar with a uniform mean scalar gradient, mixed by forced isotropic turbulence. In particular, we investigate how the odd moments of the scalar derivatives (which are the symptoms of the ramp-cliff structures) vary with $Sc$. A model based on the changing ramp-cliff structures is presented to describe the observed scaling of the scalar derivative statistics. We also address the scaling of scalar increments for varying $Sc$ and particularly explore the saturation of exponents with respect to the order of their moments.