Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 29 min ago
PreprintarXiv licencearXiv

Sparse power spectrum for passive scalars under Pierrehumbert flow

  • Alex Blumenthal
  • William Cooperman
Open at sourcePDFDOICite

Abstract

We study the long-time Fourier distribution of driven passive scalars transported by an incompressible alternating shear flow (the Pierrehumbert flow) subjected to IID random phase shifts, in the regime of strong shear-strength. With a novel and self-contained proof, we establish (i) a quantitative version of the cumulative Batchelor's law; (ii) quantitative negative regularity mixing estimates; and (iii) a strong form of `sparsity' -- unevenness in the distribution of Fourier mass in radial sectors in frequency space. Our method uses the strong shear-strength assumption to handle a purely deterministic scalar driving term.

Related

  1. Lyapunov Exponents for Passive Scalars in White-in-Time Flows
    Declan Stacy
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsDynamical systemsarXiv
  2. A Beam-Switched Sparse Circular Array for Passive Wi-Fi Sensing
    Yang Chen, Riccardo Bersan, Daniele Piazza +2
    arXivPreprintarXiv licenceFull textGeneral mathematicsarXiv
  3. Symbolic-Permutation-Based Direct Sparse Jacobian Assembly for Accelerated Power-Flow Analysis
    Tianshi Cheng, Venkata Dinavahi
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. Experimental Evaluation of a Low-Power Ultra-Wideband Receiver for Spectrum Sensing
    Panagiotis Vlachos, Ioannis A. Bartsiokas, Cedric Dehos +2
    arXivPreprintCC BY 4.0Full textGeneral mathematicsarXiv
  5. The prime spectrum of rings of integer-coefficient power series on the disk
    Jon Bannon, David Feldman
    arXivPreprintarXiv licenceFull textAlgebra & number theoryAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{blumenthal2026sparse,
  title = {{Sparse power spectrum for passive scalars under Pierrehumbert flow}},
  author = {Alex Blumenthal and William Cooperman},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31241},
  eprint = {2610.31241},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31241},
}
RIS
TY  - UNPB
TI  - Sparse power spectrum for passive scalars under Pierrehumbert flow
AU  - Alex Blumenthal
AU  - William Cooperman
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31241
UR  - https://arxiv.org/abs/2610.31241
AB  - We study the long-time Fourier distribution of driven passive scalars transported by an incompressible alternating shear flow (the Pierrehumbert flow) subjected to IID random phase shifts, in the regime of strong shear-strength. With a novel and self-contained proof, we establish (i) a quantitative version of the cumulative Batchelor's law; (ii) quantitative negative regularity mixing estimates; and (iii) a strong form of `sparsity' -- unevenness in the distribution of Fourier mass in radial sectors in frequency space. Our method uses the strong shear-strength assumption to handle a purely deterministic scalar driving term.
ER  -