Zhang, J., Dong, G. and Li, Y. orcid.org/0000-0001-7907-5176 (2017) Algorithm for transient growth of perturbations in channel Poiseuille flow. Applied Mathematics and Mechanics, 38 (11). pp. 1635-1650. ISSN 0253-4827
Abstract
This study develops a direct optimal growth algorithm for three-dimensional transient growth analysis of perturbations in channel flows which are globally stable but locally unstable. Different from traditional non-modal methods based on the Orr-Sommerfeld and Squire (OSS) equations that assume simple base flows, this algorithm can be applied to arbitrarily complex base flows. In the proposed algorithm, a re-orthogonalization Arnoldi method is used to improve orthogonality of the orthogonal basis of the Krylov subspace generated by solving the linearized forward and adjoint Navier-Stokes (N-S) equations. The linearized adjoint N-S equations with the specific boundary conditions for the channel are derived, and a new convergence criterion is pro-posed. The algorithm is then applied to a one-dimensional base flow (the plane Poiseuille flow) and a two-dimensional base flow (the plane Poiseuille flow with a low-speed streak) in a channel. For one-dimensional cases, the effects of the spanwise width of the chan-nel and the Reynolds number on the transient growth of perturbations are studied. For two-dimensional cases, the effect of strength of initial low-speed streak is discussed. The presence of the streak in the plane Poiseuille flow leads to a larger and quicker growth of the perturbations than that in the one-dimensional case. For both cases, the results show that an optimal flow field leading to the largest growth of perturbations is character-ized by high-and low-speed streaks and the corresponding streamwise vortical structures. The lift-up mechanism that induces the transient growth of perturbations is discussed. The performance of the re-orthogonalization Arnoldi technique in the algorithm for both one-and two-dimensional base flows is demonstrated, and the algorithm is validated by comparing the results with those obtained from the OSS equations method and the cross-check method.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Shanghai University and Springer-Verlag. This is an author-produced version of a paper subsequently published in Applied Mathematics and Mechanics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | transient growth; Poiseuille flow; Arnoldi method; Krylov subspace; adjoint equation |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 18 Jan 2024 11:47 |
Last Modified: | 18 Jan 2024 16:22 |
Status: | Published |
Publisher: | Springer Science and Business Media LLC |
Refereed: | Yes |
Identification Number: | 10.1007/s10483-017-2275-9 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:207833 |