Small-scale isotropy and ramp-cliff structures in scalar turbulence
Abstract
Passive scalars advected by three-dimensional Navier-Stokes turbulence exhibit a fundamental anomaly in odd-order moments because of the characteristic ramp-cliff structures, violating small-scale isotropy. We use data from direct numerical simulations with grid resolution of up to 81923 at high P\'eclet numbers to understand this anomaly as the scalar diffusivity, D, diminishes, or as the Schmidt number, Sc = /D, increases; here is the kinematic viscosity of the fluid. The microscale Reynolds number varies from 140 to 650 and Sc varies from 1 to 512. A simple model for the ramp-cliff structures is shown to characterize the scalar derivative statistics extremely well. It accurately captures how the small-scale isotropy is restored in the large-Sc limit, and additionally suggests a slight correction to the Batchelor length scale as the relevant smallest scale in the scalar field.