Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T16:01:07.345Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of compressible Ekman boundary-layer flow

Published online by Cambridge University Press:  20 April 2006

Hans Moberg ,
Lennart S. Hultgren  and
Fritz H. Bark
Hans Moberg
Affiliation:
Alfa-Laval AB, Tumba, Sweden
Lennart S. Hultgren
Affiliation:
Department of Mechanical Engineering, Illinois Institute of Technology, Chicago, IL 60616
Fritz H. Bark
Affiliation:
Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden
Get access Rights & Permissions [Opens in a new window]

Abstract

The linear stability properties of the Ekman layer in a rapidly rotating gas have been computed numerically. The two types of instability present in an Ekman layer of a homogeneous fluid, which are usually called classes A and B, respectively, are significantly modified by the compressibility. The critical Reynolds number for the class A instability is found to first increase and then decrease for increasing values of the Mach number. The instability waves of class B are monotonically destabilized as the value of the Mach number increases. In addition, a new class of unstable waves appears for a finite value of the Mach number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 147 , October 1984 , pp. 159 - 168
Copyright
© 1984 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

Batchelor, G. K. 1970 An Introduction to Fluid Dynamics. Cambridge University Press.
Caldwell, D. R. & Van Atta, C. W. 1970 Characteristics of Ekman boundary layer instabilities. J. Fluid Mech. 44, 79.Google Scholar
Faller, A. J. 1963 An experimental study of the instability of the laminar Ekman boundary layer. J. Fluid Mech. 15, 560.Google Scholar
Faller, A. J. & Kaylor, R. E. 1966 A numerical study of the instability of the laminar Ekman boundary layer. J. Atmos. Sci. 23, 53.Google Scholar
Gans, R. F. 1974 On the Poincare problem for a compressible medium. J. Fluid Mech. 62, 657.Google Scholar
Gans, R. F. 1975 On the stability of shear flows in a rotating gas. J. Fluid Mech. 68, 403.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids, 2nd edn. Cambridge University Press.
Gusev, A. & Bark, F. H. 1980 Stability of rotation-modified plane Poisseuille flow. Phys. Fluids 23, 2171.Google Scholar
Huang, K. 1963 Statistical Mechanics. Wiley.
Hultgren, L. S. 1978 Stability of axisymmetric gas flows in a rapidly rotating cylindrical container. Ph.D. thesis, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology.
Lalas, D. P. 1975 The ‘Richardson’ criterion for compressible swirling flows. J. Fluid Mech. 69, 65.Google Scholar
Lilly, D. K. 1966 On the instability of the Ekman boundary layer. J. Atmos. Sci. 23, 481.Google Scholar
Lin, C. C. 1966 The Theory of Hydrodynamic Stability. Cambridge University Press.
Miles, J. W. 1981 Waves in a rapidly rotating gas. J. Fluid Mech. 107, 487.Google Scholar
Moberg, H. 1979 Diploma thesis, Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden (in Swedish).
Morton, J. B. & Shaughnessy, E. J. 1972 Waves in a gas in solid-body rotation. J. Fluid Mech. 56, 277.Google Scholar
Nielsen, H. B. & True, H. 1978 Numerical solution of the nonlinear stability of an incompressible Ekman layer. In Numer. Meth. – 6th Intl Conf., Tblisi, USSR, 21–24 June.
Sakurai, T. & Matsuda, T. 1974 Gasdynamics of a centrifugal machine. J. Fluid Mech. 62, 727.Google Scholar
Spall, J. R. & Wood, H. G. 1984 An analysis of the stability of the compressible Ekman boundary layer. Phys. Fluids (to be published).Google Scholar
Spooner, G. F. 1982 Continuous temporal eigenvalue spectrum of an Ekman boundary layer. Phys. Fluids 25, 1958.Google Scholar
Spooner, G. F. & Criminale, W. O. 1982 The evolution of disturbances in an Ekman boundary layer. J. Fluid Mech. 115, 327.Google Scholar
Tatro, P. R. & Mollo-Christensen, E. L. 1967 Experiments on Ekman layer instability. J. Fluid Mech. 28, 531.Google Scholar
Warren, F. H. 1975 A comment on Gans' stability criterion for steady inviscid helical gas flows. J. Fluid Mech. 68, 413.Google Scholar