Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-12T21:26:01.689Z Has data issue: false hasContentIssue false
  • English
  • Français

Stability of Bödewadt flow

Published online by Cambridge University Press:  21 April 2006

ÖMer Savaş
Get access Rights & Permissions [Opens in a new window]

Abstract

Boundary-layer transition over a stationary disk in rotating flow is studied experimentally. Circular waves are observed in the boundary layer occurring on an end disk of a cylindrical cavity during impulsive spin-down to rest. The transient flow evolves into a quasi-steady regime that exhibits the properties of the Bödewadt flow. The circular waves develop in that flow. The critical Reynolds number Re = r(Ω/v)½ is determined from frequency and wavelength measurements to be about 25. The corresponding dimensionless wavenumber 2πr/ΛRe is about 0.6 and the frequency 2πf/ ΩiRe about 0.2.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 183 , October 1987 , pp. 77 - 94
Copyright
© 1987 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

Benton, E. R. 1966 On the flow due to a rotating disk. J. Fluid Mech. 24, 781–800.Google Scholar
Bödewadt, U. T. 1940 Die Drehströmung über festem Grunde. Z. Angew. Math. Mech. 20, 241–245.Google Scholar
Clarkson, M. H., Chin, S. C. & Shacter, P. 1980 Visualization of instabilities on a rotating disk. AIAA J. 18, 1541–1543.Google Scholar
Dijkstra, D. & Van Heijst, G. J. F. 1983 The flow between two finite rotating disks enclosed by a cylinder. J. Fluid Mech. 128, 123–154.Google Scholar
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 Investigations of stability and transition in rotating boundary layers. In Dynamics of Fluids and Plasmas (ed. S. I. Pai), pp. 239–255. Academic.
Faller, A. J. & Kaylor, R. E. 1967 Instability of the Ekman spiral with applications to the planetary boundary layers. Phys. Fluids Suppl. 10, S212–S219.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Gregory, H. N., Stuart, J. T. & Walker, W. S. 1955 On the stability of three dimensional boundary layers with application to the flow due to a rotating disk. Phil. Trans. R. Soc. Lond. A 248, 155–199.Google Scholar
Von Kármán, Th. 1921 Über laminare und turbulente Reibung. Z. Angew. Math. Mech. 1, 233–252.Google Scholar
Kegelman, J. T., Nelson, R. C. & Mueller, T. J. 1983 The boundary layer on an axisymmetric body with and without spin. AIAA J. 21, 1485–1491.Google Scholar
Kobayashi, R. & Izumi, H. 1983 Boundary-layer transition on a rotating cone in still fluid. J. Fluid Mech. 127, 353–364.Google Scholar
Kobayashi, R., Kohama, Y. & Kurosawa, M. 1983 Boundary-layer transition on a rotating cone in axial flow. J. Fluid Mech. 127, 341–352.Google Scholar
Kohama, Y. 1985 Flow structures formed by axisymmetric spinning bodies. AIAA J. 23, 1445–1447.Google Scholar
Kohama, Y. & Kobayashi, R. 1983 Boundary-layer transition and the behaviour of spiral vortices on rotating spheres. J. Fluid Mech. 137, 153–164.Google Scholar
Lentini, M. & Keller, H. B. 1980 The von Kármán swirling flows. SIAM J. Appl. Maths 38, 52–63.Google Scholar
Rogers, M. N. & Lance, G. L. 1960 The rotationally symmetric flow of a viscous fluid in the presence of an infinite disk. J. Fluid Mech. 7, 617–631.Google Scholar
Savaş, Ö. 1983 Circular waves on a stationary disk in rotating flow. Phys. Fluids 26, 3445–3448.Google Scholar
Savaş, Ö. 1985 On the flow visualization using reflective flakes. J. Fluid Mech. 152, 235–248.Google Scholar
Szeri, A. Z., Giron, A., Schneider, S. J. & Kaufman, H. N. 1983 Flow between rotating disks. Part 2. Stability. J. Fluid Mech. 134, 133–154.Google Scholar
Tatro, P. R. & Mollo-Christensen, E. L. 1967 Experiments on Ekman layer stability. J. Fluid Mech. 28, 531–543.Google Scholar
Weidman, P. D. 1976 On the spin-up and spin-down of a rotating fluid. Part 1. Extending the Wedemeyer model. J. Fluid Mech. 77, 685–708.Google Scholar
Wilkinson, S. P. & Malik, M. R. 1985 Stability experiments in the flow over a rotating disk. AIAA J. 23, 588–595.Google Scholar
Zandbergen, P. J. & Dijkstra, D. 1977 Non-unique solutions of the Navier-Stokes equations for the Kármán swirling flow. J. Engng Maths 11, 167–188.Google Scholar