Skip to main content Accessibility help
×
Home

The effect of mainflow transverse velocities in linear stability theory

  • T. S. Chen (a1), E. M. Sparrow (a2) and F. K. Tsou (a3)

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.

Copyright

References

Hide All
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.
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.
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.
Muller, D. E. 1956 A method for solving algebraic equations using an automatic computer. Math. Tables and Aids to Comp. 10, 208.
Reid, W. H. 1965 The stability of parallel flows. In Basic Developments in Fluid Dynamics (ed. M. Holt), pp. 249307. Academic.
Thomas, L. H. 1953 The stability of plane Poiseuille flow. Phys. Rev. 91, 780.
Tsou, F. K. & Sparrow, E. M. 1970 Hydrodynamic stability of boundary layers with surface mass transfer. Appl. Sci. Res. 22, 273.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed