Numerically measured scale-dependent eddy viscosity in homogeneous isotropic turbulence

In the present work, we report the directly measured eddy viscosity in incompressible homogeneous isotropic turbulence using the macroscopic forcing method. Our results provide a scale-dependent eddy viscosity; specifically, in the low-wavenumber-limit, eddy viscosity is a constant, while in the high-wavenumber limit, it becomes inversely proportional to the wavenumber. Our results present a contrast to the previously reported eddy diffusivity via renormalization group theories (Yakhot and Smith 1992), this difference is attributed to proper quantification of transport at small scales by large-eddies in the present study. We also report the scale-dependent turbulent Schmidt number as well as collapse of the measured eddy-viscosity operator with increase of flow Reynolds number. \newline Supported by DOE