---
_id: '2224'
abstract:
- lang: eng
  text: This work investigates the transition between different traveling helical
    waves (spirals, SPIs) in the setup of differentially independent rotating cylinders.
    We use direct numerical simulations to consider an infinite long and periodic
    Taylor-Couette apparatus with fixed axial periodicity length. We find so-called
    mixed-cross-spirals (MCSs), that can be seen as nonlinear superpositions of SPIs,
    to establish stable footbridges connecting SPI states. While bridging the bifurcation
    branches of SPIs, the corresponding contributions within the MCS vary continuously
    with the control parameters. Here discussed MCSs presenting footbridge solutions
    start and end in different SPI branches. Therefore they differ significantly from
    the already known MCSs that present bypass solutions (Altmeyer and Hoffmann 2010
    New J. Phys. 12 113035). The latter start and end in the same SPI branch, while
    they always bifurcate out of those SPI branches with the larger mode amplitude.
    Meanwhile, these only appear within the coexisting region of both SPIs. In contrast,
    the footbridge solutions can also bifurcate out of the minor SPI contribution.
    We also find they exist in regions where only one of the SPIs contributions exists.
    In addition, MCS as footbridge solution can appear either stable or unstable.
    The latter detected transient solutions offer similar spatio-temporal characteristics
    to the flow establishing stable footbridges. Such transition processes are interesting
    for pattern-forming systems in general because they accomplish transitions between
    traveling waves of different azimuthal wave numbers and have not been described
    in the literature yet.
article_number: '025503'
author:
- first_name: Sebastian
  full_name: Altmeyer, Sebastian
  id: 2EE67FDC-F248-11E8-B48F-1D18A9856A87
  last_name: Altmeyer
  orcid: 0000-0001-5964-0203
citation:
  ama: Altmeyer S. On secondary instabilities generating footbridges between spiral
    vortex flow. <i>Fluid Dynamics Research</i>. 2014;46(2). doi:<a href="https://doi.org/10.1088/0169-5983/46/2/025503">10.1088/0169-5983/46/2/025503</a>
  apa: Altmeyer, S. (2014). On secondary instabilities generating footbridges between
    spiral vortex flow. <i>Fluid Dynamics Research</i>. IOP Publishing Ltd. <a href="https://doi.org/10.1088/0169-5983/46/2/025503">https://doi.org/10.1088/0169-5983/46/2/025503</a>
  chicago: Altmeyer, Sebastian. “On Secondary Instabilities Generating Footbridges
    between Spiral Vortex Flow.” <i>Fluid Dynamics Research</i>. IOP Publishing Ltd.,
    2014. <a href="https://doi.org/10.1088/0169-5983/46/2/025503">https://doi.org/10.1088/0169-5983/46/2/025503</a>.
  ieee: S. Altmeyer, “On secondary instabilities generating footbridges between spiral
    vortex flow,” <i>Fluid Dynamics Research</i>, vol. 46, no. 2. IOP Publishing Ltd.,
    2014.
  ista: Altmeyer S. 2014. On secondary instabilities generating footbridges between
    spiral vortex flow. Fluid Dynamics Research. 46(2), 025503.
  mla: Altmeyer, Sebastian. “On Secondary Instabilities Generating Footbridges between
    Spiral Vortex Flow.” <i>Fluid Dynamics Research</i>, vol. 46, no. 2, 025503, IOP
    Publishing Ltd., 2014, doi:<a href="https://doi.org/10.1088/0169-5983/46/2/025503">10.1088/0169-5983/46/2/025503</a>.
  short: S. Altmeyer, Fluid Dynamics Research 46 (2014).
date_created: 2018-12-11T11:56:25Z
date_published: 2014-04-01T00:00:00Z
date_updated: 2021-01-12T06:56:07Z
day: '01'
department:
- _id: BjHo
doi: 10.1088/0169-5983/46/2/025503
intvolume: '        46'
issue: '2'
language:
- iso: eng
month: '04'
oa_version: None
publication: Fluid Dynamics Research
publication_identifier:
  issn:
  - '01695983'
publication_status: published
publisher: IOP Publishing Ltd.
publist_id: '4740'
quality_controlled: '1'
scopus_import: 1
status: public
title: On secondary instabilities generating footbridges between spiral vortex flow
type: journal_article
user_id: 4435EBFC-F248-11E8-B48F-1D18A9856A87
volume: 46
year: '2014'
...