Hostname: page-component-6766d58669-wvcvf Total loading time: 0 Render date: 2026-05-22T08:55:47.512Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear stability theory of oscillatory Stokes layers

Published online by Cambridge University Press:  29 March 2006

Christian Von Kerczek  and
Stephen H. Davis
Christian Von Kerczek
Affiliation:
Department of Mechanics and Materials Science, The Johns Hopkins University
Stephen H. Davis
Affiliation:
Department of Mechanics and Materials Science, The Johns Hopkins University
Get access Rights & Permissions [Opens in a new window]

Abstract

The stability of the oscillatory Stokes layers is examined using two quasi-static linear theories and an integration of the full time-dependent linearized disturbance equations. The full theory predicts absolute stability within the investigated range and perhaps for all the Reynolds numbers. A given wavenumber disturbance of a Stokes layer is found to be more stable than that of the motionless state (zero Reynolds number). The quasi-static theories predict strong inflexional instabilities. The failure of the quasi-static theories is discussed.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 62 , Issue 4 , 27 February 1974 , pp. 753 - 773
Copyright
© 1974 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.)

Article purchase

Temporarily unavailable

References

Coddington, E. A. & Levinson, N. 1955 Theory of Ordinary Differential Equations. McGraw-Hill.
Collins, J. I. 1963 J. Geophys. Res. 18, 6007.
Conrad, P. W. & Criminale, W. O. 1965 Z. angew. Math. Phys. 16, 233.
Davis, S. H. 1971 Proc. IUTAM Symp. on Unsteady Boundary Layers, Quebec.
Davis, S. H. & von Kerczek, C. 1973 Arch. Rat. Mech. Anal. 52, 112.
Dolph, C. L. & Lewis, D. C. 1958 Quart. Appl. Math. 26, 97.
Donnelly, R. J. 1964 Proc. Roy. Soc. A, 281, 130.
Drazin, P. G. & Howard, L. N. 1966 Adv. in Appl. Mech. 9, 1.
Ffowcs Williams, J. E., Rosenblat, S. & Stuart, J. T. 1969 J. Fluid Mech. 39, 547.
Gallagher, A. P. & Mercer, A. McD. 1962 J. Fluid Mech. 13, 91.
Grosch, C. E. & Salwen, H. 1968 J. Fluid Mech. 34, 177.
Isaacson, E. & Keller, H. B. 1966 Analysis of Numerical Methods. Wiley.
Kerczek, C. Von 1973 Ph.D. thesis, Department of Mechanics, Johns Hopkins University.
Kerczek, C. Von & Davis, S. H. 1972 Studies in Appl. Math. 51, 239.
Kebczek, C. Von & Davis, S. H. 1974 Pending publication.
Lambert, J. & Mitchell, A. 1962 Z. angew. Math. Phys. 13, 223.
Lapidus, L. & Seinfeld, J. H. 1971 Numerical Solutions of Ordinary Differential Equations. Academic.
Li, H. 1954 Beach Erosion Bd., U.S. Army Corps Eng., Washington, Tech. Mem. no. 47.
Longuet-Higgins, M. S. 1953 Phil. Trans. A, 245, 535.
Obremski, H. J. & Morkovin, M. V. 1969 A.I.A.A. J. 7, 1298.
O'Brien, V. & Logan, F. E. 1965 Johns Hopkins University, Appl. Physics Lab. Tech. Mem. TG-658.
Riley, N. 1966 Quart. J. Mech. Appl. Math. 19, 461.
Rosenblat, S. 1968 J. Fluid Mech. 33, 321.
Sergeev, S. I. 1966 Mekh. Zh. i Gaza, 1, 168. (Trans. Sov. Fluid Dyn.)
Shen, S. F. 1961 J. Aero. Sci. 28, 397.
Squire, H. B. 1933 Proc. Roy. Soc. A, 142, 621.
Vincent, G. E. 1957 Proc. Conf. Coast. Eng. 6. University of Florida.
Wang, C.-Y. 1965 J. Sound Vib. 2, 257.
Wilkinson, J. H. & Reinsch, C. 1971 Linear Algebra. Springer.