The Batchelor spectrum for a deterministically driven passive scalar
Analysis of PDEs
2026-03-11 v1 Dynamical Systems
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.
Cite
@article{arxiv.2603.08904,
title = {The Batchelor spectrum for a deterministically driven passive scalar},
author = {Kyle L. Liss and Jonathan C. Mattingly},
journal= {arXiv preprint arXiv:2603.08904},
year = {2026}
}
Comments
57 pages