Bifurcation of nonlinear Tollmien–Schlichting waves in a high-speed channel flow. (16th March 2018)

• Record Type: Journal Article
• Authors: Deguchi, Kengo; Walton, Andrew
• Is Part Of: Journal of fluid mechanics. Volume 843(2018)
• Page Start: 53
• Page End: 97
• Publication Date: 2018-03-16
• Subjects: bifurcation, -- high-speed flow, -- instability; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2018.137
• Languages: English
• ISSNs: 0022-1120

Abstract

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 $10^{6}$ and above, whilst for larger amplitudes our computations suggest the need for further asymptotic theories to be developed.