The effect of mainflow transverse velocities in linear stability theory

T. S. Chen, E. M. Sparrow, F. K. Tsou

Research output: Contribution to journalArticle

17 Scopus citations

Abstract

In studying the stability of the boundary layer with surface mass injection, a generalized version of the Orr–Sommerfeld equation was derived which takes account of the transverse velocity component in the mainflow. The new terms in the generalized Orr–Sommerfeld equation are inversely proportional to the Reynolds number. The resulting eigenvalue problem was solved numerically for a wide range of values of the mass injection intensity. It was found that the critical Reynolds number (based on the distance from the leading edge) decreases with increasing mass injection. The deviations between the critical Reynolds numbers from the generalized and conventional Orr–Sommerfeld equations have a different sign at low injection intensities from that at high injection intensities.

Original languageEnglish (US)
Pages (from-to)741-750
Number of pages10
JournalJournal of Fluid Mechanics
Volume50
Issue number4
DOIs
StatePublished - Dec 29 1971

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