Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-29T13:26:00.077Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow separation in a rotating annulus with bottom topography

Published online by Cambridge University Press:  20 April 2006

M. A. Page
M. A. Page
Affiliation:
School of Mathematics and Physics, University of East Anglia, Norwich NR4 7TJ, England
Get access Rights & Permissions [Opens in a new window]

Abstract

The flow in a rotating annular cylinder, of finite depth, is examined when the Rossby number Ro is O(E½), where E is the Ekman number, and when there is a topography of height O(E½) on the base of the container. The flow, relative to the rigid axial rotation, is forced by differential rotation of the lid and as it moves over the topography the streamlines are deflected parallel to the bottom surface. This induces O(1) velocity variations near the axial walls of the annulus to which the boundary layers there, of thickness O(E¼), respond. For sufficiently large values of a parameter γ ∝Ro/E½ the skin friction can vanish within these layers, with some similaritits to boundary-layer separation in a non-rotating fluid. In this study the interior flow, with horizontal viscous diffusion neglected, is calculated and used to provide a boundary condition for the, E¼ layer flow. Once λ exceeds a finite critical value a singularity is encountered in the boundary layer corresponding to flow separation from the wall. This demonstrates that E¼ layers in a rotating fluid, which for Ro = 0 have little direct influence on the interior flow, can modify the gross properties of the flow for non-zero Rossby numbers, a conclusion also reached by Walker & Stewartson (1972) in a different context.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 123 , October 1982 , pp. 303 - 313
Copyright
© 1982 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

Boyer, D. L. 1971 Rotating flow over long shallow ridges. Geophys. Fluid Dyn. 3, 165–184.Google Scholar
Buckmaster, J. 1969 Separation and magnetohydrodynamics. J. Fluid Mech. 42, 481–498.Google Scholar
Buckmaster, J. 1971 Boundary layer structure at a magnetohydrodynamic rear stagnation point. Q. J. Mech. Appl. Math. 24, 373–386.Google Scholar
Crissali, A. J. & Walker, J. D. A. 1976 Nonlinear effects for the Taylor-column for a hemisphere. Phys. Fluids 19, 1661–1668.Google Scholar
Davey, M. K. 1978 Recycling flow over bottom topography in a rotating annulus. J. Fluid Mech. 87, 497–520.Google Scholar
Goldstein, S. 1948 On laminar boundary layer flow near a position of separation. Q. J. Mech. Appl. Math. 1, 43–69.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Huppert, H. E. & Stern, M. E. 1974 The effect of side walls on homogeneous rotating flow over two-dimensional obstacles. J. Fluid Mech. 62, 417–436.Google Scholar
Keller, H. B. & Cebeci, T. 1971 Accurate numerical methods for boundary layer flows. In Proc. 2nd Int. Conf. on Numerical Methods in Fluid Dynamics (ed. M. Holt). Lecture Notes in Physics, vol. 8, pp. 92–100, Springer.
Leibovich, S. 1967 Magnetohydrodynamic flow at a rear stagnation point. J. Fluid Mech. 29, 401–413.Google Scholar
Maxworthy, T. 1977 Topographic effects in rapidly-rotating fluids: flow over a transverse ridge. Z. angew. Math. Phys. 28, 853–864.Google Scholar
Page, M. A. 1981 Rotating fluid flows at low Rossby numbers. Ph.D. thesis, University of London.
Page, M. A. 1982 A numerical study of detached shear layers in a rotating sliced cylinder. Geophys. Astrophys. Fluid Dyn. (to appear).
Stewartson, K. 1957 On almost rigid rotations. J. Fluid Mech. 3, 17–26.Google Scholar
Walker, J. D. A. & Stewartson, K. 1972 The flow past a circular cylinder in a rotating frame. Z. angew. Math. Phys. 23, 745–752.Google Scholar
Walker, J. D. A. & Stewartson, K. 1974 Separation and the Taylor-column problem for a hemisphere. J. Fluid Mech. 66, 767–789.Google Scholar