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arXiv · 2603.08904

The Batchelor spectrum for a deterministically driven passive scalar

Kyle L. Liss·Jonathan C. Mattingly
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Abstract

We study the long-time behavior of a passive scalar transported by an incompressible flow in the presence of smooth, deterministic forcing. For a specific spatially Lipschitz and time-periodic velocity field, we prove that all sufficiently smooth initial data is attracted to a limiting solution that satisfies a cumulative form of Batchelor's law. To our knowledge, this provides the first example for which a version of Batchelor's law can be established with deterministic forcing.

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Kyle L. Liss, Jonathan C. Mattingly. 2026-03-09. The Batchelor spectrum for a deterministically driven passive scalar. https://arxiv.org/abs/2603.08904

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