Bifurcation of nonlinear Tollmien-Schlichting waves in a high-speed channel flow
File(s)
Accepted version
Author(s)
Deguchi, Kengo
Walton, AG
Type
Journal Article
Abstract
Plane Poiseuille flow has long served as the simplest testing ground for Tollmien–Schlichting wave instability. In this paper, we provide a comprehensive comparison of equilibrium Tollmien–Schlichting wave solutions arising from new high-resolution Navier–Stokes calculations and the corresponding predictions of various large-Reynolds-number asymptotic theories developed in the last century, such as double-deck theory, viscous nonlinear critical layer theory and strongly nonlinear critical layer theory. In the relatively small to moderate amplitude regime, the theories excellently predict the behaviour of the numerical solutions at Reynolds numbers of order and above, whilst for larger amplitudes our computations suggest the need for further asymptotic theories to be developed.
Date Issued
2018-05-25
Date Acceptance
2018-01-21
Citation
Journal of Fluid Mechanics, 2018, 843, pp.53-97
ISSN
0022-1120
Publisher
Cambridge University Press (CUP)
Start Page
53
End Page
97
Journal / Book Title
Journal of Fluid Mechanics
Volume
843
Copyright Statement
© 2018 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Subjects
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
bifurcation
high-speed flow
instability
PLANE POISEUILLE FLOW
HIGH-REYNOLDS-NUMBER
BOUNDARY-LAYERS
PARALLEL FLOWS
COUETTE-FLOW
SHEAR FLOWS
COHERENT STRUCTURES
INTERACTION STATES
STABILITY
DISTURBANCES
01 Mathematical Sciences
09 Engineering
Fluids & Plasmas
Publication Status
Published
Date Publish Online
2018-03-16