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 |∇θ|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 81923. The Reλ spans 140−1000, and Sc≡ν/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 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 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 Reλ increases
Versions
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BibTeX
@misc{mishi2026scalar,
title = {{Scalar gradient structure and dynamics in turbulent mixing at high Reynolds and Schmidt numbers}},
author = {Ruqaiya Islam Mishi and Dhawal Buaria},
howpublished = {arXiv},
year = {2026},
month = jun,
doi = {10.48550/arxiv.2606.07858},
eprint = {2606.07858},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.07858},
}
RIS
TY - UNPB
TI - Scalar gradient structure and dynamics in turbulent mixing at high Reynolds and Schmidt numbers
AU - Ruqaiya Islam Mishi
AU - Dhawal Buaria
PY - 2026
DA - 2026/06/05
PB - arXiv
DO - 10.48550/arxiv.2606.07858
UR - https://arxiv.org/abs/2606.07858
AB - How well turbulence mixes a scalar θ is governed by the scalar dissipation rate χ= 2D |∇θ|^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≡ν/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
ER -