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- Title
A self-sustaining mechanism for plane Couette flow with a flexible lower boundary.
- Authors
Chotai, A; Walton, A G
- Abstract
The stability of plane Couette flow to travelling-wave disturbances is studied asymptotically at high Reynolds numbers Re when the lower boundary possesses a degree of flexibility modelled by a spring-backed plate. First, it is shown that a three-dimensional (3D) linear instability exists, with streamwise and spanwise wavelengths comparable with the channel width. Building on this, nonlinear effects from the self-interaction of the wave are introduced, leading to a self-sustaining interaction between a roll/streak flow and the 3D wave. Governing nonlinear vortex-wave interaction (VWI) equations are derived and a perturbation analysis is carried out to guide a numerical investigation of the equations. The co-existence of two families of finite-amplitude solutions, each with different flow structures, is found. Numerical solutions of the VWI equations in each case show that a small wave amplitude of O (Re − 1 (log Re) − 1 / 2) is all that is necessary to provoke an O (1) change to the basic Couette flow.
- Subjects
COUETTE flow; NUMERICAL solutions to equations; REYNOLDS number; MODULATIONAL instability
- Publication
Quarterly Journal of Mechanics & Applied Mathematics, 2023, Vol 76, Issue 3, p371
- ISSN
0033-5614
- Publication type
Article
- DOI
10.1093/qjmam/hbad009