Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T12:20:00.470Z Has data issue: false hasContentIssue false
  • English
  • Français

Curvature- and rotation-induced instabilities in channel flow

Published online by Cambridge University Press:  26 April 2006

O. John E. Matsson  and
P. Henrik Alfredsson
O. John E. Matsson
Affiliation:
Department of Gas Dynamics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
P. Henrik Alfredsson
Affiliation:
Department of Gas Dynamics, Royal Institute of Technology, S-100 44 Stockholm, Sweden
Get access Rights & Permissions [Opens in a new window]

Abstract

In a curved channel streamwise vortices, often called Dean vortices, may develop above a critical Reynolds number owing to centrifugal effects. Similar vortices can occur in a rotating plane channel due to Coriolis effects if the axis of rotation is normal to the mean flow velocity and parallel to the walls. In this paper the flow in a curved rotating channel is considered. It is shown from linear stability theory that there is a region for which centrifugal effects and Coriolis effects almost cancel each other, which increases the critical Reynolds number substantially. The flow visualization experiments carried out show that a complete cancellation of Dean vortices can be obtained for low Reynolds number. The rotation rate for which this occurs is in close agreement with predictions from linear stability theory. For curved channel flow a secondary instability of travelling wave type is found at a Reynolds number about three times higher than the critical one for the primary instability. It is shown that rotation can completely cancel the secondary instability.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 210 , January 1990 , pp. 537 - 563
Copyright
© 1990 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

Alfredsson, P. H. & Persson, H. 1989 Instabilities in channel flow with system rotation. J. Fluid Mech. 202, 543.Google Scholar
Andereck, C. D., Lui, S. S. & Swinney, H. L. 1986 Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155.Google Scholar
Brewster, D. P., Grosberg, P. & Nissan, A. H. 1959 The stability of viscous flow between horizontal concentric cylinders. Proc. R. Soc. Lond. A251, 76.Google Scholar
Coles, D. 1965 Transition in circular Couette flow. J. Fluid Mech. 21, 385.Google Scholar
Craik, A. D. D. 1985 Wave Interactions and Fluid Flows. Cambridge University Press.
Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic Stability. Cambridge University Press.
Finlay, W. H., Keller, J. B. & Ferziger, J. H. 1988 Instability and transition in curved channel flow. J. Fluid Mech. 194, 417.Google Scholar
Gibson, R. D. & Cook, A. E. 1974 The stability of curved channel flow. Q. J. Mech. Appl. Maths. 27, 149.Google Scholar
Hart, J. E. 1971 Instability and secondary motion in a rotating channel flow. J. Fluid Mech. 45, 341.Google Scholar
Hughes, T. H. & Reid, W. H. 1964 The effect of a transverse pressure gradient on the stability of Couette flow. Z. Angew. Math. Phys. 15, 573.Google Scholar
Lezius, D. K. & Johnston, J. P. 1976 The structure and stability of turbulent boundary layers in rotating channel flow. J. Fluid Mech. 77, 153.Google Scholar
Ligrani, P. M. & Niver, R. D. 1988 Flow visualization of Dean vortices in a curved channel with 40 to 1 aspect ratio. Phys. Fluids 31, 3605.Google Scholar
Oswatitsch, K. & Wieghardt, K. 1987 Ludwig Prandtl and his Kaiser-Wilhelm-Institut. Ann. Rev. Fluid Mech. 19, 1.Google Scholar
Raney, D. C. & Chang, T. S. 1971 Oscillatory modes of instability for flow between rotating cylinders with a transverse pressure gradient. Z. Angew. Math. Phys. 22, 680.Google Scholar
Rasena, S., Busse, F. H. & Rehberg, I. 1989 A theoretical and experimental study of double-layer convection. J. Fluid Mech. 199, 519.Google Scholar
Reid, W. H. 1958 On the stability of viscous flow in a curved channel. Proc. R. Lond. Soc. A244, 186.Google Scholar
Savas, ö. 1985 On flow visualization using reflective flakes. J. Fluid Mech. 152, 235.Google Scholar
Schlichting, H. 1979 Boundary Layer Theory, 7th edn. McGraw-Hill.
Tritton, D. J. & Davies, P. A. 1985 Instabilities in geophysical fluid dynamics In Hydrodynamic Instabilities and the Transition to Turbulence. Topics in Applied Physics, vol. 45, 2nd edn. Springer.
Yang, K. & Kim, J. 1988 Transition in plane Poiseuille flow with system rotation. Bull. Am. Phys. Soc. 33, 2284.Google Scholar