On the Problem of Resonant Incompressible Flow in Ventilated Double Glazing

T. Akinaga*, T. M. Harvey-Ball, T. Itano, S. C. Generalis, E. C. Aifantis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Abstract: We employ a homotopy method, rather than conventional stability theory, in order to resolve the degeneracy due to resonance, which exists in fluid motion associated with a channel of infinite extent in ventilated double glazing. The introduction of a symmetry breaking perturbation, in the form of a Poiseuille flow component, alters substantially the resonant bifurcation tree of the original flow. Previously unknown resonant higher order nonlinear solutions, i.e. after the removal of the perturbative Poiseuille flow component, are discovered. A possible extension of the methodology to consider non-Newtonian gradient enhanced incompressible viscous fluids is also briefly discussed.

Original languageEnglish
Pages (from-to)1753-1767
Number of pages15
JournalLobachevskii Journal of Mathematics
Volume42
Issue number8
DOIs
Publication statusPublished - 5 Sep 2021

Bibliographical note

Funding Information:
TA acknowledges the financial support from the Horizon 2020 Marie Sklodowska Curie Programme of the European Union. SG acknowledges financial support from ORDIST of Kansai University. TI acknowledges an International Collaboration fund from Aston University. THB acknowledges a research studentship from EPSRC DtP 2020. This work was also funded by the RISE-2018–824022-ATM2BT of the European H2020-MSCA programme. Finally, ECA acknowledges the support of Friedrich-Alexander University of Erlangen–Nuremberg, grant no. 377472739/GRK 2423/1-2019 and a Mercator Fellow post.

Publisher Copyright:
© 2021, Pleiades Publishing, Ltd.

Keywords

  • bifurcation theory
  • gradient fluid
  • homotopy method
  • incompressible flow
  • nonlinearity
  • stability

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