Neutral stability curves of compressible Görtler flow generated by low-frequency free-stream vortical disturbances

Pre-transitional compressible boundary layers perturbed by low-frequency free-stream vortical disturbances and flowing over plates with streamwise-concave curvature are studied via matched asymptotic expansions and numerically. The Mach number, the Görtler number and the frequency of the free-stream...

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Bibliographic Details
Published in:Journal of fluid mechanics 2019-10, Vol.876, p.1146-1157
Main Authors: Viaro, Samuele, Ricco, Pierre
Format: Article
Language:English
Subjects:
Agreements
Asymptotic series
Boundary conditions
Boundary layer transition
Boundary layers
Compressibility
Computational fluid dynamics
Curvature
Decks
Disturbances
Flow mapping
Flow stability
Fluid flow
Graphs
JFM Papers
Kinematics
Mach number
Neutral stability curves
Reynolds number
Rivers
Theory
Viscosity
Vortices
Waves
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Summary:Pre-transitional compressible boundary layers perturbed by low-frequency free-stream vortical disturbances and flowing over plates with streamwise-concave curvature are studied via matched asymptotic expansions and numerically. The Mach number, the Görtler number and the frequency of the free-stream disturbance are varied to obtain the neutral stability curves, i.e. curves in the space of the parameters that distinguish spatially growing from spatially decaying perturbations. The receptivity approach is used to calculate the evolution of Klebanoff modes, highly oblique Tollmien–Schlichting waves influenced by the concave curvature of the wall, and Görtler vortices. The Klebanoff modes always evolve from the leading edge, the Görtler vortices dominate when the influence of the curvature becomes significant and the Tollmien–Schlichting waves may precede the Görtler vortices for moderate Görtler numbers. For relatively high frequencies the triple-deck formalism allows us to confirm the numerical result of the negligible influence of the curvature on the Tollmien–Schlichting waves when the Görtler number is an order-one quantity. Experimental data for compressible Görtler flows are mapped onto our neutral-curve graphs and earlier theoretical results are compared with our predictions.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2019.590