---
_id: '12146'
abstract:
- lang: eng
  text: 'In this paper, we explore the stability and dynamical relevance of a wide
    variety of steady, time-periodic, quasiperiodic, and chaotic flows arising between
    orthogonally stretching parallel plates. We first explore the stability of all
    the steady flow solution families formerly identified by Ayats et al. [“Flows
    between orthogonally stretching parallel plates,” Phys. Fluids 33, 024103 (2021)],
    concluding that only the one that originates from the Stokesian approximation
    is actually stable. When both plates are shrinking at identical or nearly the
    same deceleration rates, this Stokesian flow exhibits a Hopf bifurcation that
    leads to stable time-periodic regimes. The resulting time-periodic orbits or flows
    are tracked for different Reynolds numbers and stretching rates while monitoring
    their Floquet exponents to identify secondary instabilities. It is found that
    these time-periodic flows also exhibit Neimark–Sacker bifurcations, generating
    stable quasiperiodic flows (tori) that may sometimes give rise to chaotic dynamics
    through a Ruelle–Takens–Newhouse scenario. However, chaotic dynamics is unusually
    observed, as the quasiperiodic flows generally become phase-locked through a resonance
    mechanism before a strange attractor may arise, thus restoring the time-periodicity
    of the flow. In this work, we have identified and tracked four different resonance
    regions, also known as Arnold tongues or horns. In particular, the 1 : 4 strong
    resonance region is explored in great detail, where the identified scenarios are
    in very good agreement with normal form theory. '
acknowledgement: "This work was supported by the Spanish MINECO under Grant Nos. FIS2017-85794-P
  and PRX18/00179, the Spanish MICINN through Grant No. PID2020-114043GB-I00, and
  the\r\nGeneralitat de Catalunya under Grant No. 2017-SGR-785. B.W.’s research was
  also supported by the Chinese Scholarship Council through Grant CSC No. 201806440152."
article_number: '114111'
article_processing_charge: No
article_type: original
author:
- first_name: B.
  full_name: Wang, B.
  last_name: Wang
- first_name: Roger
  full_name: Ayats López, Roger
  id: ab77522d-073b-11ed-8aff-e71b39258362
  last_name: Ayats López
  orcid: 0000-0001-6572-0621
- first_name: A.
  full_name: Meseguer, A.
  last_name: Meseguer
- first_name: F.
  full_name: Marques, F.
  last_name: Marques
citation:
  ama: Wang B, Ayats López R, Meseguer A, Marques F. Phase-locking flows between orthogonally
    stretching parallel plates. <i>Physics of Fluids</i>. 2022;34(11). doi:<a href="https://doi.org/10.1063/5.0124152">10.1063/5.0124152</a>
  apa: Wang, B., Ayats López, R., Meseguer, A., &#38; Marques, F. (2022). Phase-locking
    flows between orthogonally stretching parallel plates. <i>Physics of Fluids</i>.
    AIP Publishing. <a href="https://doi.org/10.1063/5.0124152">https://doi.org/10.1063/5.0124152</a>
  chicago: Wang, B., Roger Ayats López, A. Meseguer, and F. Marques. “Phase-Locking
    Flows between Orthogonally Stretching Parallel Plates.” <i>Physics of Fluids</i>.
    AIP Publishing, 2022. <a href="https://doi.org/10.1063/5.0124152">https://doi.org/10.1063/5.0124152</a>.
  ieee: B. Wang, R. Ayats López, A. Meseguer, and F. Marques, “Phase-locking flows
    between orthogonally stretching parallel plates,” <i>Physics of Fluids</i>, vol.
    34, no. 11. AIP Publishing, 2022.
  ista: Wang B, Ayats López R, Meseguer A, Marques F. 2022. Phase-locking flows between
    orthogonally stretching parallel plates. Physics of Fluids. 34(11), 114111.
  mla: Wang, B., et al. “Phase-Locking Flows between Orthogonally Stretching Parallel
    Plates.” <i>Physics of Fluids</i>, vol. 34, no. 11, 114111, AIP Publishing, 2022,
    doi:<a href="https://doi.org/10.1063/5.0124152">10.1063/5.0124152</a>.
  short: B. Wang, R. Ayats López, A. Meseguer, F. Marques, Physics of Fluids 34 (2022).
date_created: 2023-01-12T12:06:58Z
date_published: 2022-11-04T00:00:00Z
date_updated: 2023-10-03T11:07:58Z
day: '04'
department:
- _id: BjHo
doi: 10.1063/5.0124152
external_id:
  isi:
  - '000880665300024'
intvolume: '        34'
isi: 1
issue: '11'
keyword:
- Condensed Matter Physics
- Fluid Flow and Transfer Processes
- Mechanics of Materials
- Computational Mechanics
- Mechanical Engineering
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://upcommons.upc.edu/handle/2117/385635
month: '11'
oa: 1
oa_version: Submitted Version
publication: Physics of Fluids
publication_identifier:
  eissn:
  - 1089-7666
  issn:
  - 1070-6631
publication_status: published
publisher: AIP Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: Phase-locking flows between orthogonally stretching parallel plates
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 34
year: '2022'
...