Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-18T17:43:19.418Z Has data issue: false hasContentIssue false
  • English
  • Français

The effect of mainflow transverse velocities in linear stability theory

Published online by Cambridge University Press:  29 March 2006

T. S. Chen ,
E. M. Sparrow  and
F. K. Tsou
T. S. Chen
Affiliation:
University of Missouri-Rolla, Rolla, Missouri
E. M. Sparrow
Affiliation:
University of Minnesota, Minneapolis, Minnesota
F. K. Tsou
Affiliation:
Drexel University, Philadelphia, Pennsylvania
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 4 , 29 December 1971 , pp. 741 - 750
Copyright
© 1971 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alekseev, Yu. N. & Korotkin, A. I. 1966 Effect of transverse stream velocity in an incompressible boundary layer on the stability of the laminar flow regime. Fluid Dynamics, 1, 21.Google Scholar
Barry, M. D. J. & Ross, M. A. S. 1970 The flat plate boundary layer. Part 2. The effect of increasing thickness on stability. J. Fluid Mech. 43, 813.Google Scholar
Fu, T. S. 1967 Viscous instability of asymmetrical parallel flows in channels. Ph.D. Thesis, University of Minnesota.
Hughes, T. H. & Reid, W. H. 1956 On the stability of the asymptotic suction boundary-layer profile. J. Fluid Mech. 23, 715.Google Scholar
Muller, D. E. 1956 A method for solving algebraic equations using an automatic computer. Math. Tables and Aids to Comp. 10, 208.Google Scholar
Reid, W. H. 1965 The stability of parallel flows. In Basic Developments in Fluid Dynamics (ed. M. Holt), pp. 249–307. Academic.
Thomas, L. H. 1953 The stability of plane Poiseuille flow. Phys. Rev. 91, 780.Google Scholar
Tsou, F. K. & Sparrow, E. M. 1970 Hydrodynamic stability of boundary layers with surface mass transfer. Appl. Sci. Res. 22, 273.Google Scholar