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Long wavelength streamwise vortices caused by wall curvature or roughness. (English) Zbl 1502.76036

Summary: Long wavelength instabilities of boundary layers caused by centrifugal effects or wall roughness are investigated. The wall roughness is modelled by small amplitude surface waviness. The instability is described in the nonparallel regime where it develops on the same length scale as the unperturbed flow. It is shown that instabilities initiated by disturbances close to the leading edge initially deform rapidly into algebraically growing eigensolutions but then deform into exponentially growing disturbances. The disturbances ultimately develop in a quasi-parallel manner and then pass successively through the high Görtler number, or equivalent large roughness parameter, regimes first described by J. P. Denier et al. [On the receptivity problem for Görtler vortices: vortex motions induced by wall roughness. Techn. Rep. 90-31, Nasa Contractor ICASE (1990); Philos. Trans. R. Soc. Lond., Ser. A 335, No. 1636, 51–85 (1991; Zbl 0850.76211)]. It is shown that the mode which develops downstream is the most rapidly growing one available and not the second most unstable mode as claimed in a recent paper.

MSC:

76E09 Stability and instability of nonparallel flows in hydrodynamic stability
76F06 Transition to turbulence

Citations:

Zbl 0850.76211
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Full Text: DOI

References:

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