Scalar gradient structure and dynamics in turbulent mixing at high Reynolds and Schmidt numbers

Abstract

How well turbulence mixes a scalar $θ$ is governed by the scalar dissipation rate $χ= 2D |\nablaθ|^2$, making scalar gradients central to turbulent mixing. We study the structure and amplification of these gradients for passive scalars driven by a uniform mean-gradient in isotropic turbulence, using DNS at grid resolutions up to $8192^3$. The $Re_λ$ spans $140-1000$, and $Sc\equivν/D$ spans $1-512$. We analyze joint statistical correlations of velocity and scalar gradients that underlie scalar-gradient amplification. Unconditional statistics reaffirm earlier observations that production of $χ$ is dominated by nonlinear amplification of scalar gradients by strain-rate. Scalar gradients preferentially align with the most compressive strain eigenvector and remain orthogonal to vorticity, with both trends virtually independent of $Re_λ$ and $Sc$. Conditional statistics reveal that this organization becomes dramatically enhanced in regions of intense scalar dissipation: scalar gradient becomes near-perfectly aligned with the most compressive eigendirection and orthogonal to other eigendirections and vorticity. This and visualizations suggest that intense scalar dissipation is organized in sheet-like structures formed in shear layers between vortex tubes, where intense strain also generally resides. However, the effective strain acting along intense scalar gradients is comparatively much weaker, indicating intense scalar dissipation arises primarily from optimal alignments rather than intense strain alone. Molecular diffusion arrests intense scalar-gradient events primarily by redistributing scalar-gradient variance away from intense structures. The contribution from imposed mean-gradient is negligible,but still imprints anisotropy directly onto smallest scales via the strain field. The statistics broadly become universal as $Sc$ and $Re_λ$ increases