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arXiv · 2503.05885

Fourier mass lower bounds for Batchelor-regime passive scalars

William Cooperman·Keefer Rowan
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Abstract

Batchelor predicted that a passive scalar $\psi^\nu$ with diffusivity $\nu$, advected by a smooth fluid velocity, should typically have Fourier mass distributed as $|\hat \psi^\nu|^2(k) \approx |k|^{-d}$ for $|k| \ll \nu^{-1/2}$. For a broad class of velocity fields, we give a quantitative lower bound for a version of this prediction summed over constant width annuli in Fourier space. This improves on previously known results, which require the prediction to be summed over the whole ball.

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William Cooperman, Keefer Rowan. 2025-03-07. Fourier mass lower bounds for Batchelor-regime passive scalars. https://arxiv.org/abs/2503.05885

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