PreprintCC BY 4.0arXiv
Optimal Linear Inviscid Damping and Vorticity Depletion for Non-monotonic shear flows
Abstract
We give a proof of optimal pointwise linear inviscid damping and vorticity depletion for a large class of spectrally stable shear flows b(y) on the rectangular torus. This extends the linear inviscid estimates in \cite{CJWZ25} for Kolmogorov flow b(y) =cos y using completely different methods. Crucially, both methods remove an apparent logarithmic correction to the depletion and inviscid damping rates. Our method combines pointwise bounds for a parametrix with an explicit solution of a simpler inner problem which makes the removal of the logarithm clear.
Related
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BibTeX
@misc{beekie2026optimal,
title = {{Optimal Linear Inviscid Damping and Vorticity Depletion for Non-monotonic shear flows}},
author = {Rajendra Beekie and Shan Chen and Hao Jia},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08912},
eprint = {2610.08912},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08912},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Optimal Linear Inviscid Damping and Vorticity Depletion for Non-monotonic shear flows
AU - Rajendra Beekie
AU - Shan Chen
AU - Hao Jia
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08912
UR - https://arxiv.org/abs/2610.08912
AB - We give a proof of optimal pointwise linear inviscid damping and vorticity depletion for a large class of spectrally stable shear flows b(y) on the rectangular torus. This extends the linear inviscid estimates in \cite{CJWZ25} for Kolmogorov flow b(y) =cos y using completely different methods. Crucially, both methods remove an apparent logarithmic correction to the depletion and inviscid damping rates. Our method combines pointwise bounds for a parametrix with an explicit solution of a simpler inner problem which makes the removal of the logarithm clear.
ER -