Hostname: page-component-78c5997874-94fs2 Total loading time: 0 Render date: 2024-11-10T07:30:37.886Z Has data issue: false hasContentIssue false
  • English
  • Français

An algorithmic approach to the linear stability of the Ekman layer

Published online by Cambridge University Press:  20 April 2006

Mogens V. Melander
Mogens V. Melander
Affiliation:
Laboratory of Applied Mathematical Physics and Institute for Numerical Analysis. Technical University of Denmark
Get access Rights & Permissions [Opens in a new window]

Abstract

The linear stability of the stationary Ekman-layer flow near a plane boundary is considered. Analytical formulas for the eigenfunctions are derived by a spectral analysis. Standard optimization algorithms are used to calculate critical points, maximum growth rates and neutral-stability curves. The near approach provides a better basis for both a linear and a nonlinear stability analysis than the well-known methods have done. The method may also be applied to other boundary-layer problems.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 132 , July 1983 , pp. 283 - 293
Copyright
© 1983 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

Faller, A. J. 1963 An experimental study of the instability of the laminar Ekman boundary layer J. Fluid Mech. 15, 560–576.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, 466–480.Google Scholar
Iooss, G., Nielsen, H. B. & TRUE, 1978 Bifurcation of the stationary Ekman layer flow into a stable periodic flow Arch. Rat. Mech. Anal. 68, 227–256.Google Scholar
Lilly, D. K. 1966 On the instability of Ekman boundary flow. J. Atmos. Sci. 23, 481–494 (1966).Google Scholar
Powell, M. J. D. 1970 A hybrid method for non-linear equations. In Numerical Methods for Non-linear Algebraic Equations (ed. P. Rabinowitz), pp. 87–114. Gordon & Breach.
Powell, M. J. D., 1978 A fast algorithm for non-linearly constrained optimization calculations. In Proc. Biennial Conf. on Numerical Analysis, Dundee, 1977 (ed. G. A. Watson). Lecture Notes in Mathematics, vol. 630, pp. 144–187. Springer.
Roesner, K. G. 1979 An analytical approach to the determination of neutral stability curves. In Recent Developments in Theoretical and Experimental Fluid Mechanics (ed. U. Müller, K. G. Roesner & B. Schmidt), pp. 339–345. Springer.