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

Ruqaiya Islam Mishi1 and Dhawal Buaria1,2,*

  • *Contact author: dhawal.buaria@ttu.edu
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Phys. Rev. Fluids 11, 104610 – Published 22 October, 2026

DOI: https://doi.org/10.1103/3xd3-p8lc

Abstract

How well turbulence mixes a scalar θ is ultimately governed by the scalar dissipation rate χ=2D|∇θ|2, where D is the scalar diffusivity, making scalar gradients central to turbulent mixing. We study the structure and amplification of these gradients for the canonical problem of passive scalar driven by a uniform mean gradient in stationary isotropic turbulence, using well-resolved direct numerical simulations at grid resolutions up to 81923. The Taylor-scale Reynolds number Reλ spans 140–1000, and the Schmidt number Sc≡ν/D spans 1–512, where ν is the kinematic viscosity. We analyze joint statistical correlations of velocity and scalar gradients that underlie scalar-gradient amplification. Unconditional statistics reaffirm earlier observations that production of scalar dissipation 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 Reλ 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 strain eigendirection and orthogonal to the other strain eigendirections and to vorticity. This geometry, also supported by visualizations, suggests that intense scalar dissipation is organized in sheetlike 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 conditional statistics broadly exhibit progressively weaker Sc dependence as Reλ increases, demonstrating convergence towards an asymptotic state governing the local structure and dynamics of intense scalar dissipation.

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Phys. Rev. Fluids 11, 104610– Published 22 October, 2026
  • Received 5 June 2026
  • Accepted 7 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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