Convection induced by instabilities in the presence of a transverse seepage

Takeshi Akinaga, Tomoaki Itano, Sotirios Generalis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The transition of laterally heated flows in a vertical layer and in the presence of a streamwise pressure gradient is examined numerically for the case of different values Prandtl number. The stability analysis of the basic flow for the pure hydrodynamic case ( Pr = 0 ) was reported in [1]. We find that in the absence of transverse pumping the previously known critical parameters are recovered [2], while as the strength of the Poiseuille flow component is increased the convective motion is delayed considerably. Following the linear stability analysis for the vertical channel flow our attention is focused on a study of the finite am- plitude secondary travelling-wave (TW) solutions that develop from the perturbations of the transverse roll type imposed on the basic flow and temperature profiles. The linear stability of the secondary TWs against three-dimensional perturbations is also examined and it is shown that the bifurcating tertiary flows are phase-locked to the secondary TWs.
Original languageEnglish
Pages (from-to)533–543
Number of pages11
JournalChaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena
Volume91
Early online date4 Aug 2016
DOIs
Publication statusPublished - Oct 2016

Bibliographical note

© 2016, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/

Keywords

  • non-linear fluid dynamics
  • Floquet theory
  • stability
  • bifurcation theory

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